# Calculate the following integral and determine whether it's convergent, or divergent. integral at [-3,0] x dx / sqr(9 - x^2)

91,530 results

1. ### Calculus

Calculate the following integral and determine whether it's convergent, or divergent. integral at [-3,0] x dx / sqr(9 - x^2)
2. ### Calculus

Use the Comparison Theorem to determine whether the following integral is convergent or divergent. S= integral sign b=infinity and a=1 S(9(cosx^2))/ (1+x^2) dx
3. ### calculus

Determine whether the integral is convergent or divergent.If it is convergent, evaluate it. from 0 to infinity e^(-y^1/2)dy
4. ### calculus

Determine whether the integral is convergent or divergent.If it is convergent, evaluate it. form -infinity to 0 x/(x^4+25)dx
5. ### calculus (integral test)

use integral test to determine whether the series is convergent or divergent infinity (sum symbol) n=1 1/(sqrt n)^5
6. ### Calculus

Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral.
7. ### calculus

Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. from -infinity to infinity 17xe^(-x^2)dx
8. ### calculus

is this correct? use the integral test to determine if this series is convergent or divergent: the series from n=2 to infinity of 1/(n*square root of (ln(n))) I said it was divergent because the integral went to infinity
9. ### calculus

use the integral test to determine whether the series is convergent or divergent ∑ n=9 1/n(ln n)^3
10. ### calculus

Determine whether the following is convergent of divergent. integral(lower limit=0, upper limit=infinity)of sin(x)sin(x^2)dx Thanks
11. ### Calculus

Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral, at the following particular step. I know I need to take the ...
12. ### Calculus

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it and enter that value as your answer. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity, state your answer as "...
13. ### Calculus

Determine if convergent or divergent: Integral 1 to infinity of e to the power of (-1/2).
14. ### Calculus

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it and enter that value as your answer. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity, state your answer as "...
15. ### Calculus

Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE. sum from 1 to infinity of 1/e^2n. It is convergent, but I do not know how to solve for the sum.
16. ### Convergent/Divergent

determine whether the series 1 + 1/2^5 + 1/3^5 + 1/4^5 +...is convergent or divergent? How do I tell the difference?
17. ### Calculus 2 (Series - Convergent or Divergent?)

Can someone show me a step by step process and explanation how to solve this problem? 1) Consider the following series. (∞ on top of summation symbol) (k = 1 under the summation symbol) ∑ k(k+15)/(k+13)^2 Determine whether the series is convergent or divergent. If ...
18. ### Calculus

Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE. sum from 1 to infinity of (5^n+4^n)/20^n It is convergent, but I do not know how to find the sum.
19. ### Calculus

integral -oo, oo [(2x)/(x^2+1)^2] dx (a) state why the integral is improper or involves improper integral *infinite limit of integration (b) determine whether the integral converges or diverges converges? (c) evaluate the integral if it converges I know f(x)=arctan->f'(x)=1...
20. ### calculus

Determine whether the series is convergent o divergent and say what test you used to solve it. (d) sum n=1 to infinity (5n)^(3n) / (5^n + 3)^n (e) sum k=1 to infinity 5 / sqr(2k - 1)
21. ### calculus

show that an integral of the form ∫00,a e^(-px) dx is convergent if p>0 and divergent if p<0
22. ### Calculus

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as INF. If it diverges to negative infinity, state your answer as MINF. If it diverges without being infinity or negative infinity, state ...
23. ### Calculus II

I need to find if the summation of (n^4)/(n^10 + 1) is convergent or divergent from n=1 to infinity. I tried splitting it up into two sums, one being 1/n^6, which would be convergent because p=6>1, and then the other being n^4, but I'm not sure how to know if this is ...
24. ### Calculus

Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. A (sub n)=((4n-7)/(4n+9))
25. ### Calculus

If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a to b of g of x dx ~the integral from a to a of...
26. ### Calculus

Show that the following integral is convergent, Integral, it goes from 0 to infinity dx/(sqrt(x) + x^2)
27. ### calculus

1. integral -oo, oo [(2x)/(x^2+1)^2] dx 2. integral 0, pi/2 cot(theta) d(theta) (a) state why the integral is improper or involves improper integral (b) determine whether the integral converges or diverges converges? (c) evaluate the integral if it converges CONFUSE: how would...
28. ### calc asap!

can you help me get started on this integral by parts? 4 S sqrt(t) ln(t) dt 1 please help! thanks! Integral t^(1/2)Ln(t)dt = 2/3 t^(3/2)Ln(t)- 2/3 Integral t^(1/2) dt = 2/3 t^(3/2)Ln(t) - 4/9 t^(3/2) Simpler method: Integral t^(a)dt = t^(a+1)/(a+1) Integral d/da [t^(a)]dt = d/...
29. ### Quick calc question

If f(x) and g(x) are continuous on [a, b], which one of the following statements is false? the integral from a to b of the sum of f of x and g of x, dx equals the integral from a to b of f of x, dx plus the integral from a to b of g of x dx the integral from a to b of the ...
30. ### calc 2

Determine whether the integral converges or diverges. Find the value of the integral if it converges. The integral where b=2 and a=0 (x/x^2-1 dx).
31. ### Calculus II/III

A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the x-axis from 4 to 9. For part B of our question , the surface of revolution ...
32. ### calculus

how do you solve the integral of 1/[(square root of x)(lnx)] from 2 to infinity? i did the p- integral theorem with 1/square root of x and got it to be a divergent integral. however i was told this was the wrong way and that i should do it by integration by parts. but i can't ...
33. ### Math/Calculus

How would I solve the following integral with the substitution rule? Integral of: [(x^3)*(1-x^4)^5]dx Put 1-x^4 = y Then -4x^3 dx = dy Integral is then becomes: Integral of -1/4 y^5 dy ok, thanks a lot! I got it now.
34. ### Calculus

This is a definite integral question. Evaluate the following integral: (0)S(a)((x)((a^2 - x^2)^(1/2)))dx with a being a constant and the (0) being at the bottom of the integral notation and (a) at the top. S is the integral notation. I firstly checked whether the function was ...
35. ### calc

I was given a decreasing concave down graph of the integral F(x) from 0-8. i have to say whether the following are greater then, less then,equal to, or unable to determine each other 1. T (greater then) M 2. T (greater then) R 3. M (less then) S 4. S ? actual integral where t=...
36. ### CALC

I was given a decreasing concave down graph of the integral F(x) from 0-8. i have to say whether the following are greater then, less then,equal to, or unable to determine each other 1. T (greater then) M 2. T (greater then) R 3. M (less then) S 4. S ? actual integral where t=...
37. ### Definite integral by parts (correction)

Hello, I just wanted to verify if my work was good. Calculate the following integral by parts: ∫ upper limit is 1/5 and lower limit is 1/10. of 10sin^-1 (5x)dx so first I named the variables: u = 10 sin^-1 (5x) du = 50 / sqr(1-25x^2) dv = dx v = x so we get: = 10 sin^-1...
38. ### calc

how do you start this problem: integral of xe^(-2x) There are two ways: 1) Integration by parts. 2) Differentiation w.r.t. a suitably chosen parameter. Lets do 1) first. This is the "standard method", but it is often more tedious than 2) You first write the integral as: ...
39. ### calculus

8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the cross-section perpendicular to the y-axis is a square. Set up a definite integral expressing the volume of the solid. Answer choices: integral from -4 to 4 of 4(16-y^2)dy, integral from -4 to 4 of (16+y^2)dy...
40. ### Calculus

Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, x=0, and y=0 (a) integral (x^2)^2 from 0 to 2=32/5...
41. ### Integral Calculus - Series

Find if series is convergent or divergent. Series from n=2 to infinity (4n+7)/(3n^3 -8n)
42. ### Pre-calculus

Which of the following series is divergent? a) 1+3(1/4)+9(1/4)^2+27(1/4)^3... b) 1+3(1/5)+9(1/5)^2+27(1/5)^3... c) 1+3(1/7)+9(1/7)^2+27(1/7)^3... d) 1+3(1/2)+9(1/2)^2+27(1/2)^3... How do you determine if a series in convergent or divergent??? The book that I have is about as ...
43. ### calculus

Use the ratio test to determine whether the series is convergent or divergent. 1/2 + 2^2/2^2 + 3^2/2^3 + 4^2/2^4 + ...
44. ### Calculus

Determine whether the sequence is divergent or convergent. a(sub n)=(−1)^n(sin(2/n))
45. ### Integral

That's the same as the integral of sin^2 x dx. Use integration by parts. Let sin x = u and sin x dx = dv v = -cos x du = cos x dx The integral is u v - integral of v du = -sinx cosx + integral of cos^2 dx which can be rewritten integral of sin^2 x = -sinx cos x + integral of (...
46. ### calculus

There are four integrals: 1) definite integral x/(1+x^4)dx b/w 0_infinity 2) definite integral (x^2)/(1+x^4)dx b/w 0_infinity 3) definite integral (x^3)/(1+x^4)dx b/w 0_infinity 4) definite integral (x^4)/(1+x^4)dx b/w 0_infinity Which of these integrals converge. First of all...
47. ### calculus

There are four integrals: 1) definite integral x/(1+x^4)dx b/w 0_infinity 2) definite integral (x^2)/(1+x^4)dx b/w 0_infinity 3) definite integral (x^3)/(1+x^4)dx b/w 0_infinity 4) definite integral (x^4)/(1+x^4)dx b/w 0_infinity Which of these integrals converge. First of all...
48. ### calculus

use the comparison test to determine whether the series is convergent or divergent ∑ n=1 1/n^n
49. ### integration by parts

s- integral s ln (2x+1)dx ? = ln(2x+1)x - s x d( ln (2x+1)) = ln(2x+1)x- s x [(2x+1)'/ (2x+1)] dx = ln(2x+1)x- s x [(2)/ (2x+1)] ?... then i'm confused... "ln(2x+1)x- s x [(2)/ (2x+1)] ?... then i'm confused..." x [(2)/ (2x+1)] = 2x/(2x+1) = (2x+1-1)/(2x+1) = 1-1/(2x+1) B.t.w...
50. ### Quick calc question

Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 – x2 and the x-axis? the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x square, dx the ...
51. ### Quick calc question

Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 – x2 and the x-axis? the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x square, dx the ...
52. ### Quick calc question

Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 – x2 and the x-axis? the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x square, dx the ...
53. ### Math/Calculus

How would I evaluate the following integral by using integration by parts? Integral of: (t^3)(e^x)? You mean (x^3)(e^x)? x^3 exp(x) dx = x^3 d[exp(x)] = d[x^3 exp(x)] - exp(x) d[x^3] = d[x^3 exp(x)] - 3 x^2 exp(x) dx So, if you integrate this you get x^3 exp(x) - 3 Integral of...
54. ### calculus (please with steps and explanations)

consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: (a) definite integral from 0(on the ...
55. ### Calculus

Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 – x2 and the x-axis? the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x square, dx the ...
56. ### calculus

LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find the integral from 1 to 3 of f(x)dx in terms of ...
57. ### calculus

LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find the integral from 1 to 3 of f(x)dx in terms of ...
58. ### math

LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find the integral from 1 to 3 of f(x)dx in terms of ...
59. ### Calculus (urgent help)

consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: (a) definite integral from 0(on the ...
60. ### Calculus II

Integrate using integration by parts (integral) (5-x) e^3x u = 5-x du = -dx dv = e^3x v = 3e^3x I wonder if this is right so far. = uv - (integral) v du = (5-x)(3e^3x) - (integral) (-3e^3x) =(5-x)(3e^3x) + (integral) (3e^3x) = (5-x)(3e^3x) + 9e^3x + C
61. ### Calculus 2

Determine whether the series is convergent, absolutely convergent, conditionally convergent, or divergent. On top of the summation sign (∑) is infinity. Under the summation sign is n=2, and right next to it (to the right of ∑ sign) is (n root of (n)-1)^n (Sorry I ...
62. ### math

Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral 2(2x+6)^5 dx, u=2x+6
63. ### math

Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral cos(9x) dx, u=9x
64. ### calculus

is the sum from k=1 to infinity of 1/(k^2+1) convergent? i said it was because the integral is convergent
65. ### calculus

consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: (a) definite integral from 0(on the ...
66. ### Calculus

Which of the following is a step in evaluating. (Integral) cos^2 5x dx A. (Integral) 1+cos10x/2 dx B. (Integral) 1-cos10x/2 dx C. (Integral) 1+cos10x/20 dx D. (Integral) 1-cos10x/20 dx
67. ### Calculus

Hello, I'd appreciate any help with the following question below: Information: g(x)= 4 (x+1)^(-2/3) f(x)= ∫ g(t) dt The Question: What is f(26) ? (NOTE: I don't know how to do this on a key board, so I'll just say that while I did type an Indefinite integral for "f(x)" it is...
68. ### Calc 2

Determine whether the series is convergent or divergent series symbol n=1 to infinity (n^2/(e^(3n))
69. ### Calc 121

How do you integrate using substitution: the integral from 1 to 3 of: ((3x^2)+(2))/((x^3)+(2x)) There is a trick to this one that grealy simplifies the integral. Let u = x^3 + 2x. Then du = (3x^2 + 2)dx The integral then bemoces just the integral of du/u, which is ln u = ln (x...
70. ### mathematics

calculate the following integral: Perform a change of variable and integrate the following elliptical integral I = Square root [(1-x^2)*(2-x)] limits between -1 to 1 please showing any working
71. ### calc

find integral using table of integrals ) integral sin^4xdx this the formula i used integral sin^n xdx =-1/n sin^n-1xcosx +n-1/n integral sin^n-2 using the formula this is what i got: integral sin^4xdx=-1/4sin^3xcosx+3/4 integral sin^2xdx= -1/2sinxcosx+1/2 integral 1 dx can ...
72. ### Calculus

which of the following is equivalent to integral (a,b) k*f(x)+C)dx where k and C are constants k integral (a,b)(f(x)+C)dx ***** intergral (a,b)kdx + intergral (a,b)f(x)dx+ intergral (a,b) Cdx k integral (a,b)f(x)+ integral (a,b) Cdx integral (a,b) kdx * integral (a,b) f(x) dx...
73. ### Calculus 2

Use the Comparison Test to determine whether the series is convergent or divergent. On top of the summation sign (∑) is infinity. Under the summation sign is n=1, and right next to it (to the right of ∑ sign) is cos^2n/n^2. How would I compare them and come to the ...
74. ### Calculus

Use the symmetry of the graphs of the sine and cosine functions as an aid in evaluating each definite integral. (a) Integral of sinx*dx from -pi/4 to pi/4 (b) Integral of cosx*dx from -pi/4 to pi/4 (c) Integral of cosx*dx from -pi/2 to pi/2 (d) Integral of sinx*cosx*dx from -...
75. ### Math

Find the integrals. (show steps) (integral sign) xe^(4x^2) I think this how is how its done: (integral sign) xe^(4x^2) it's a u du problem let u=4x^2 so, du=8x dx now you have an x already so all u need is 8 inside and and 1/8 outside the integral [1/8] (integral sign) [8]xe^(...
76. ### Integral Help

I need to find the integral of (sin x)/ cos^3 x I let u= cos x, then got -du= sin x (Is this right correct?) I then rewrote the integral as the integral of -du/ u^3 and then rewrote that as the integral of - du(u^-3). For this part, I wasn't sure how to finish. I was hoping to...
77. ### Calculus

For what values of p>0 does the series Riemann Sum [n=1 to infinity] 1/ [n(ln n) (ln(ln n))^p] converge and for what values does it diverge? You need to let the summation start at n = 3 to avoid the singularity at n = 1 (although you can formally take denominator to b ...
78. ### calculus

Use the ratio test to determine whether each series is convergent or divergent. 4/(1*2*3) + 8/(1*2*3*4) + 16(1*2*3*4*5) + ... How exactly do I do this? The example problem says to first find the nth term, but I don't know how. Help is much appreciated.
79. ### Calculus

I was able to solve (e), this is the only one I don't get. Determine whether the series is convergent or divergent and say what test you used to solve it. (d) sum n=1 to infinity (5n)^(3n) / (5^n + 3)^n
80. ### double integral

1. Sketch the region of integration & reverse the order of integration. Double integral y dydz... 1st (top=1, bottom =0)... 2nd(inner) integral (top=cos(piex), bottom=(x-2)... 2. Evaluate the integral by reversing the order of integration. double integral sqrt(2+x^3) dxdy... ...
81. ### calc II

Express the integrals as the sum of partial fractions and evaluate the integral: (integral of) (x^2)dx/(x-1)(x^2 +2x+1) My work: The above integral is equal to x^2dx/(x+1)^2 (A/x-1) + (B/x+1) + (Cx+D)/(x+1)^2 = x^2 A(x+1)^2 + B(x-1)(x+1) + (Cx+d)(x-1) = x^2 Ax^2 + 2Ax + A + Bx...
82. ### Calculus

Hello, I have some calculus homework that I can't seem to get started..at least not on the right track? I have 3 questions 1. integral of [(p^5)*(lnp)dp] I'm using the uv-integral v du formula So first, I'm finding u and I think it's lnp.......so du is 1/p Then, I think dv = p...
83. ### Calc BC

1. Find the indefinite integral. Indefinite integral tan^3(pix/7)sec^2(pix/7)dx 2. Find the indefinite integral by making the substitution x=3tan(theta). Indefinite integral x*sqrt(9+x^2)dx 3. Find the indefinite integral. Indefinite integral cos(x)sin^3(x)dx
84. ### Integral calculus

You have not proved to me that the Integral of lnsinx w.r.t.x from 0 to pi/2 is equal to:Integral of lnsinx w.r.t.x from 0 to pi/4 plus Integral of lncosx w.r.t.x from 0 to pi/4.
85. ### calculus

how do you determine the convergence of : definite integral from 1--> infinity of lnx/(x^3)? i set the problem as lim (R--->infinity) of the integral of lnx/(x^3) from 1--->R, but i can't compute the integral.
86. ### Math

Calculate the integrals if they converge. 10.) Integral from 1 to infinity of X/4+X^2 dx 14.) integral from Pi/2 to Pi/4 of Sin X / sqrt cos x dx 22.) integral from 0 to 1 of ln x/x dx I'm having problems with working these out to figure out if they converge or not. Any help ...
87. ### Math - Algebra2

state whether the series is convergent or divergent 1) 3 + 12 + 48 + ... 2) 4 + 4/5 + 4/25 + ...
88. ### Definite Integral

Calculate the following integral: upper limit: 1 lower limit: -2 ∫ (5x + 3) / (x^2 + 4x + 7) dx Do I do a polynomial division for this one? Thank you
89. ### calculus

consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value of the integral as N-->infinity? Does ...
90. ### calculus

consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value of the integral as N-->infinity? Does ...
91. ### Calc 2

a. Integral (x^2)/(sqrt(1+(x^2))) Would I separate these two into 2 separate integrals? Like: Integral of x^2 and the other integral of 1/sqrt(1+(x^2)) b. Integral (x^7)/(ln(x^4))dx Do I use integration by parts for this? I put u= lnx du = 1/x dv = x^7 v = (x^8)/8 It doesn't ...
92. ### calculus

calculate the indefinite integral 2sec^2x dx (cosx)/(sin^3x) dx calculate the definite integral interval pi/4, pi/12 csc2xcot2x dx

evaluate the integral integral of 3 to 2 x/(x^2-2)^2 dx u=x^2-2 du=2x dx 1/2 du = x dx integral of 1/u^2 du -1/(x^2-2) Then I plug in 3 and 2 and subtract them form each other -1/(3^2-2) - (-1/(2^2-2) Is this correct?
94. ### Calculus 2

The question is: Evaluate the improper integral for a>0. The integral is: the integral from 0 to infinity, of e^(-y/a)dy Can anyone help me solve this? When I try I get 'a', which apparently is incorrect. Thank you!
95. ### math

Evaluate the given integral, where C is the circle with positive orientation. Cauchy integral theorem, integral over C (2z-3)/(z^(2)-4)(z+2) dz, C:|z+3|=3
96. ### math

evaluate the double integral and reverse order of integration [(first integral 0 to 1)(second integral 9y to 9)e^(x^2)dx)dy
97. ### Calculus

Can someone look over my work and tell me if my steps look correct? I'm trying to correct some problems that looked wrong. Instructions: Find the total areas between the given curves. 1. x= (y^3) and x=(y^2) on the interval [0,1] (integral from 0 to 1 of) ((y^3)-(y^2))dy = (...
98. ### Calculus

evaluate the integral or state that it diverges. Check if I did it correctly. integral 0,1 dr/r^.999 lim b->0+ integral b, 1 1000r^.001 =-1000
99. ### math

How do I derive the secant reduction rule? Integral (sec x)^n dx = Integral (sec x)^(n-2) * (sec x)^2 dx = Integral ((tan x)^2 + 1)^(n/2-1) * (sec x)^2 dx Doing a substitution with: u = tax x du = (sec x)^2 dx = Integral (u^2 + 1)^(n/2-1) * du At this point I'm stuck. Any ...
100. ### Calculus - Integrals

I have 3 questions, and I cannot find method that actually solves them. 1) Integral [(4s+4)/([s^2+1]*([S-1]^3))] 2) Integral [ 2*sqrt[(1+cosx)/2]] 3) Integral [ 20*(sec(x))^4 Thanks in advance.