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

20,920 results
  1. 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^6-5 dx, u = x6 − 5 I got the answer 1/6ln(x^6-5)+C but it was wrong. ps. I wrote the word

  2. 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;

  3. 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

  4. 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.)

  5. 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

  6. Calculus Please Help2

    Evaluate the integral by using substitution. Use an upper-case "C" for the constant of integration. integral x^5((x^6-2)^10)dx ty

  7. Please help with Calc!

    Evaluate the indefinite integral. integral 2e^(2x)sin(e^2x) Note: Use an upper-case "C" for the constant of integration.

  8. calc 1

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

  9. 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) =

  10. math

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

  11. 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

  12. Calculus :)

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

  13. Calculus

    What is the best method to evaluate the integral of 1/(4x^2-9) 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

  14. 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.

  15. 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

  16. 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).

  17. calculus

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

  18. 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

  19. 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,√(1-x^2 -y^2)]∫𝑧√(x^2 +y^2 +z^2)dz dy dx into anequivalent integral in spherical coordinates and evaluate the integral.

  20. 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

  21. Calculus

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

  22. 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

  23. 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

  24. 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.

  25. 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

  26. 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

  27. Calculus

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

  28. 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,

  29. 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

  30. 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

  31. 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

  32. 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 (1-x^4))dx I don't

  33. Math (Integrals)

    Find the indefinite integral in two ways. ∫(2x-1)^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 =(2x-1)^3/6 + C What would be

  34. calculus

    Suppose R is the rectangle 1

  35. 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.

  36. 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(u-1)u^(1/2)du. u=?

  37. 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

  38. 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

  39. 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

  40. 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

  41. 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

  42. 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

  43. 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

  44. 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

  45. 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)

  46. 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

  47. 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

  48. 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

  49. 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^2x-1)(tanx) dx then i did a u substitution u = secx du

  50. 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^2x-1)(tanx) dx then i did a u substitution u = secx du

  51. 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

  52. 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?

  53. Calculus

    Solve these indefinite and definite integrals. [integration sign] 4j-5j^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

  54. Calculus

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

  55. caculus

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

  56. Math(Please check)

    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?

  57. 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.

  58. 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

  59. 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!!

  60. 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.

  61. Business Calculus

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

  62. 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

  63. Calculus AB

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

  64. Calculus Please Help

    Evaluate the indefinite integral Note: Use an upper-case "C" for the constant of integration. integral sqrt(100x^2-400)/x dx Ty

  65. calculus

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

  66. 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,

  67. calculus

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

  68. calculus

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

  69. calculus

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

  70. Calc

    Evaluate the following indefinite integral integral of the funtion (x^3)/(x^2-49)dx

  71. Calculus II

    Evaluate using u-substitution: Integral of: 4x(tan(x^2))dx Integral of: (1/(sqrt(x)*x^(sqrt(x))))dx Integral of: (cos(lnx)/x)dx

  72. 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 [1-cos (4x)] dx, but then i'm confused. The indefinite integral of (1/2) [1-cos

  73. 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

  74. Math

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

  75. 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?

  76. calculus

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

  77. integration (calculus)

    Find the indefinite integral. ∫((e^-x-1)/(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?

  78. 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

  79. Calculus

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

  80. 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

  81. calculus

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

  82. 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!

  83. Calculus

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

  84. calculus

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

  85. calculus

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

  86. calculus

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

  87. Calculus

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

  88. Calculus

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

  89. Calc

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

  90. calculus

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

  91. 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

  92. 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

  93. 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

  94. calculus

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

  95. Calculus

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

  96. Calculus (please help)

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

  97. calculus

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

  98. Calculus

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

  99. 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?

  100. 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

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