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
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calculus integrals
Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.) integral x^5/x^65 dx, u = x6 − 5 I got the answer 1/6ln(x^65)+C but it was wrong. ps. I wrote the word

calculus
1.Evaluate the integral. (Use C for the constant of integration.) integral ln(sqrtx)dx 2. Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given axis. y = 4ex, y = 4e−x, x = 1;

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

Calculus
1. Express the given integral as the limit of a Riemann sum but do not evaluate: integral[0 to 3]((x^3  6x)dx) 2.Use the Fundamental Theorem to evaluate integral[0 to 3]((x^3  6x)dx).(Your answer must include the antiderivative.)

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

Calculus Please Help2
Evaluate the integral by using substitution. Use an uppercase "C" for the constant of integration. integral x^5((x^62)^10)dx ty

Please help with Calc!
Evaluate the indefinite integral. integral 2e^(2x)sin(e^2x) Note: Use an uppercase "C" for the constant of integration.

calc 1
Evaluate the indefinite integral. e^(8x)sin(e^(8x))

calc II
Express the integrals as the sum of partial fractions and evaluate the integral: (integral of) (x^2)dx/(x1)(x^2 +2x+1) My work: The above integral is equal to x^2dx/(x+1)^2 (A/x1) + (B/x+1) + (Cx+D)/(x+1)^2 = x^2 A(x+1)^2 + B(x1)(x+1) + (Cx+d)(x1) =

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

Math
(i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in parts (i) and (ii) are the

Calculus :)
Use the substitution x=2tan(theta) to evaluate the indefinite integral 53dx/(x^2sqrt(x2+4))

Calculus
What is the best method to evaluate the integral of 1/(4x^29) dx a) Integration by parts b) Rewrite the integral using long division c) Rewrite the integral using partial fractions d) Use a substitution > my answer Can you check for me, please

Calculus
"Evaluate the following indefinite integrals: "S" (3x^2 2)/(x^3  2x + 1)^3 dx" We're practicing the substitution rule, and I know how to do it, but I don't know what/how to substitute in this question. btw: "S" is the integral sign.

math
Note: You can get full credit for this problem by just answering the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. Consider the definite integral from

Calculus II
1) Compute the indefinite integral: integral 2x ln(x^2  8x + 18) dx 2) Note that x^4 + 1 = (x^4 + 2x^2 + 1) = (x^2 + 1)^2  (sqrt2x)^2 ... use this trick to compute the following indefinite integral as an elementary function (with exact coefficients).

calculus
Use the indicated substitution to evaluate the integral integral 18sec(2x) tan(2x)dx, u=2x

calc 3
1. Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 36x^2+25y^2=1. L= double integral R (4sin(144x^2+100y^2) dA. 2. Use the given transformation to evaluate the

Calculus
online class and I don't know what to do so I posts. Any help is great.Thank you Convert the integral [0,1]∫ [0,√(1x^2 y^2)]∫𝑧√(x^2 +y^2 +z^2)dz dy dx into anequivalent integral in spherical coordinates and evaluate the integral.

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

Calculus
9)Evaluate the indefinite integral. ∫x^8e^(x^9)dx

Math
Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: integral[4,1] sqrt(1+(dy/dx)^2) dy/dx

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 xaxis from 4 to 9. For part B of our question , the surface

Math
1. Evaluate the indefinite integral ([6x^2 + 12x^(3/2) +4x+9]/sqrt x)dx. Answer = + C 2. Evaluate the indefinite integral (12sin x+4tan x)dx. Answer = + C 3. Evaluate the indefinite integral. (x^7)e^(x^8)dx. Answer = + C Thank you for helping.

Question on Integration
(i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in parts (i) and (ii) are the

calculus
a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1]. i) Write out the contour integral ∫γ f(z)dz as an integral with respect to t. You do not need to evaluate this integral. ii) Evaluate the integral ∫0,1+i z^2dz iii) What is the relationship between

Calculus
Use the substitution x=3tan() to evaluate the indefinite integral 93dx/(x^2sprt(x^2+9))

Calculus
I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5(u^2))du I have a feeling I will be able to find the derivative easily,

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

Math
1. Evaluate the indefinite integral integral symbol[6x5+2sec(x) tan(x)]dx. 2. Integral symbol 8 at the top, 5 at the bottom 3x2+3x2 dx = Thanks

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

Calculus
Hello Everyone, I need help with Calc II. 1. Integral from 0 to 1 of (sin(3*pi*t))dt For this one, I got 1/3pi cos (9 pi^2) + 1/3pi 2. indefinite integral of sinxcos(cosx)dx I got sin(cosx) + C 3. Indefinite integral of x over (root (1x^4))dx I don't

Math (Integrals)
Find the indefinite integral in two ways. ∫(2x1)^2 dx The first way I used was using the power rule and chain rule with substitution. Let u = 2x  1 du = 2 dx (1/2)∫ u^2 du (Applying power rule) (1/2) * (u^3/3) + C =(2x1)^3/6 + C What would be

calculus
Suppose R is the rectangle 1

Math/Calculus
How would I solve the following integral with the substitution rule? Integral of: [(x^3)*(1x^4)^5]dx Put 1x^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.

Math
In the exercise we want to use a substitution to integrate integral xsqrt(x+1)dx. Find the substitution u to transform the integral into integral(u1)u^(1/2)du. u=?

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 uvintegral v du formula So first, I'm finding u and I think it's lnp.......so du is 1/p

calculus
We're doing indefinite integrals using the substitution rule right now in class. The problem: (integral of) (e^6x)csc(e^6x)cot(e^6x)dx I am calling 'u' my substitution variable. I feel like I've tried every possible substitution, but I still haven't found

Calculus
Would someone clarify this for me... Is antiderivatives just another name for intergral and why is intergral of a function is the area under the curve? Antiderivatives is another word for integral. Why area? THink on this...the integral is the sum of all

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

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

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

Calc
Evaluate the integral using any method: (Integral)sec^3x/tanx dx I started it out and got secx(1tan^2x)/tanx. I know I just have to continue simplifying and finding the integral, but I'm stuck on the next couple of steps. Also, I have another question

calculus
8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the crosssection perpendicular to the yaxis is a square. Set up a definite integral expressing the volume of the solid. Answer choices: integral from 4 to 4 of 4(16y^2)dy, integral from

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)

Math (Definite Integrals)
Sketch the region given by the definite integral. Use geometric shapes and formulas to evaluate the integral (a > 0, r > 0). r ∫ sqrt(r^2  x^2) dx r While I recognize that this looks similar to a circle function, I'm not sure how to graph and evaluate

math
How do I derive the secant reduction rule? Integral (sec x)^n dx = Integral (sec x)^(n2) * (sec x)^2 dx = Integral ((tan x)^2 + 1)^(n/21) * (sec x)^2 dx Doing a substitution with: u = tax x du = (sec x)^2 dx = Integral (u^2 + 1)^(n/21) * du At this

Math
Consider the following indefinite integral. I= ∫ tan(x)sec^2(x) dx Part 1 of the question was to evaluate I using substitution, u=sec(x) my answer: (sec^2(x))/2 +C Part 2: evaluate I using substitution, u=tan(x) my answer: tan^2(x)/2 + C Part 3 is to

Calc
Hello im trying to integrate tan^3 dx i have solved out the whole thing but it doesnt match up with the solution.. this is what i did: first i broke it up into: integral tan^2x (tanx) dx integral (sec^2x1)(tanx) dx then i did a u substitution u = secx du

Calc
Hello im trying to integrate tan^3 dx i have solved out the whole thing but it doesnt match up with the solution.. this is what i did: first i broke it up into: integral tan^2x (tanx) dx integral (sec^2x1)(tanx) dx then i did a u substitution u = secx du

Calculus
Find the volume of the solid whose base is the region in the xyplane bounded by the given curves and whose crosssections perpendicular to the xaxis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, x=0, and y=0 (a) integral

MATH
Evaluate the indefinite integral. (Use theta for ƒÆ.) ç(8ƒÆ + cos(7ƒÆ))dƒÆ Ans: blank + C C is constant. How do I evaluate it?

Calculus
Solve these indefinite and definite integrals. [integration sign] 4j5j^3 dj I got 2j^2  5/4j^4... is this my final answer? If j is the variable, for the indefinite integral you have to add a constant. For the definite integral, you have to put in the

Calculus
Evaluate the indefinite integral. (e^7x)/(e^14x+16)dx

caculus
Evaluate the indefinite integral. ∫(arcsinx)^6/(1−x^2)^(1/2)dx

Math(Please check)
evaluate the integral integral of 3 to 2 x/(x^22)^2 dx u=x^22 du=2x dx 1/2 du = x dx integral of 1/u^2 du 1/(x^22) Then I plug in 3 and 2 and subtract them form each other 1/(3^22)  (1/(2^22) Is this correct?

Calculus URGENT test tonight
Integral of: __1__ (sqrt(x)+1)^2 dx The answer is: 2ln abs(1+sqrt(x)) + 2(1+sqrt(X))^1 +c I have no clue why that is! Please help. I used substitution and made u= sqrt(x)+1 but i don't know what happened along the way! Your first step was a good one.

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

Calc
Use substitution to evaluate the indefinite integral: The integral of [ (sq. root (1 + ln x)) ((ln x)/x) dx] Im confused on what i should substitute u and du for. Thank you so much!!

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.

Business Calculus
Evaluate each indefinite integral. Use the substitution method. X square root (x+3) dx

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

Calculus AB
Evaluate the indefinite integral of (ln(x))/(x + xln(x)) dx by using variable substitution. Show all steps of your work.

Calculus Please Help
Evaluate the indefinite integral Note: Use an uppercase "C" for the constant of integration. integral sqrt(100x^2400)/x dx Ty

calculus
Evaluate the indefinite integral. integral of 8 sin^4 x cos x dx

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,

calculus
evaluate the indefinite integral integral sign [8/x ln(1x)] dx = +c

calculus
Evaluate the indefinite integral. integral of 4e^(4x)sin[e^(4x)]dx

calculus
evaluate the indefinite integral integral sign [8/(x ln(1x))] dx = ?????+c

Calc
Evaluate the following indefinite integral integral of the funtion (x^3)/(x^249)dx

Calculus II
Evaluate using usubstitution: Integral of: 4x(tan(x^2))dx Integral of: (1/(sqrt(x)*x^(sqrt(x))))dx Integral of: (cos(lnx)/x)dx

trig integration
s integral endpoints are 0 and pi/2 i need to find the integral of sin^2 (2x) dx. i know that the answer is pi/4, but im not sure how to get to it. i know: s sin^2(2x)dx= 1/2 [1cos (4x)] dx, but then i'm confused. The indefinite integral of (1/2) [1cos

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

Math
good day please help with this indefinite integral,especially what formula i can use to solve it2x+1/(3x^2+3x+5)dx.Find the indefinite integral.

Calculus
"Evaluate the following indefinite integral using integration by parts: *integral sign* tan^1(x) dx" I let u = tan^1(x) and dv = dx. Is that right?

calculus
use substitution to find the indefinite integral (x^3+3x)(x^4+6x^2+8)^9dx

integration (calculus)
Find the indefinite integral. ∫((e^x1)/(e^x + x)^2) dx I am trying to use the substitution method. u=e^x + x du= e^x+1 dx Right so far?

Calculus
int(dx/(x^2+9)) u = x/3 Use the indicated substitution (above) to evaluate the integral. Confirm answer by differentiation. Okay, so I found that du/dx is 1/3. dx is 3du. Just by looking at the integral I can tell this is some form of tan^1(x), if we

Calculus
Can someone help me to integrate by substitution the indefinite integral: (sinx)/ (1+cos(^2)x)?

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

calculus
evaluate integral or state that it is diverges integral oo, 2 [2/(x^21)] dx  integral oo, 2 [2/(x^21)] dx Through partial fractions, I came up with lim [ln(x1)ln(x+1)] b, 2 b>oo I get (ln(3)0)(oooo)). The

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!

Calculus
Evaluate the indefinite integral ¡Ò(x2)^3/x^2 dx

calculus
evaluate the indefinite integral of ((x+4)/(17+8x+x^2))dx

calculus
Evaluate the indefinite integral: y*(y+5)^1/3 dy.

calculus
Evaluate the indefinite integral: (8e^x)dx

Calculus
Evaluate the indefinite integral: x^2 / (34x^3)^6 I got 1/(60(4x^33))^5 but it's not right.

Calculus
Evaluate the indefinite integral 1.((x^4 2 +x)3x^1)

Calc
Evaluate the indefinite integral (3/x^6)4√(x^2)

calculus
Evaluate the indefinite integral: ((4/x^5)+(4/7x))dx

math
Evaluate the given integral, where C is the circle with positive orientation. Cauchy integral theorem, integral over C (2z3)/(z^(2)4)(z+2) dz, C:z+3=3

Calculus
Can someone check my work and answer? Evaluate the integral from 1 to 0 of (4x^6+2x)^3(12x^5+1)dx My work: let u=4x^6+2x dx=du/24x^5+2 now we have the integral from 1 to 0 of u^3(12x^5+1)(du/24x^5+2) Simplifies to the integral from 1 to 0 of

Calc.
Evaluate the indefinite integral. Please check my work? Not sure if I am doing this correctly. S= integral symbol S x^3*sqrt(x^2 + 1) dx u = x^2+1 x^2= u  1 du = 2xdx du/2 = xdx 1/2 S x^2 * x sqrt (x^2 + 1) du 1/2 S (u  1) * sqrt (u) du multiply square

calculus
evaluate the indefinite integral of (9xe^4x^2)dx

Calculus
Evaluate the indefinite integral: INT dx/(64+x^2)^2

Calculus (please help)
Evaluate the indefinite integral: INT dx/(64+x^2)^2 Please help with this one.

calculus
Evaluate the indefinite integral: y^3*sqrt(y + 5) dy.

Calculus
Evaluate the indefinite integral: ∫ from 1 to 2 of ln (x²e^x) dx Thank you for your help!!

Calculus
U substitution on indefinite integral/antiderivative. (t^3+4)^2 t^2 On this should I use u on the parenthesis and should I put this into a natural log?

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