Calculus

How do you integrate [(x^2)(cos(2(x^3)))]? I tried to integrate by parts but I'm going in circles yet again...

  1. 👍
  2. 👎
  3. 👁
  1. Let w = 2x^3
    6x^2 dx = dw
    The integral becomes the integral of
    (1/6)w cos w, which can be solved using integration by parts to give
    (1/6)[cos w + w sin w]
    = (1/6)[cos(2x^3) + 2x^2 sin(2x^3)]

    1. 👍
    2. 👎
  2. Wouldn't it simply be
    (1/6)sin(2x^3) + c ?

    1. 👍
    2. 👎
  3. The derivative of Reiny's answer is
    (1/6)cos(2x^3)*6x^2 = x^2 cos(2x^3), so I must have made a mistake somewhere.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    find the volume bounded by the parabolic cylinder z=4-x^2 and the planes x=0, y=0, y=6 and z=0 I just want some help figuring out the limits of this question : So for z, we have to integrate from z=0 to z=4-x^2 (am i right?)

  2. math, calculus 2

    Consider the area between the graphs x+y=16 and x+4= (y^2). This area can be computed in two different ways using integrals. First of all it can be computed as a sum of two integrals integrate from a to b of f(x)dx + integrate

  3. physics (mechanics)

    Practice problem: A rocket sled for testing equipment under large accelerations starts at rest and accelerates according to the expression: a= (2.8 m/s^3)t + (3.9 m/s^2) How far does the rocket move in the time interval t=0 to

  4. Calculus

    Use Simpson's rule with n = 4 to approximate. Keep at least 2 decimal places accuracy. Integrate: (cos(x))/(x) x=1 to 5

  1. calculus

    integrate it by integrating factor (cos^3x)dy/dx +ycosx=sinx

  2. possible functions

    How to find all possible functions of f with a given derivative. 1. f'(x) = 2 2. f'(x) = sinx Integrate each function. Remember that there can be an arbitrarcontant C added to each integral. 1. f(x) = x + C 2. f(x) = -cos x + C We

  3. Integral calculus

    Please do help solve the followings 1) Integrate e^4 dx 2) Integrate dx/sqrt(90^2-4x^2) 3) Integrate (e^x+x)^2(e^x+1) dx 4) Integrate xe^x2 dx e^4 is a constant. 3) let u= e^x + x du= (e^x + 1)dx 4) let u= x du=dx v= e^x dv= e^x

  4. Calculus

    6.] Replace the integral in exercise 5 (int. (1/ 1 – t) dt a = 0, b = 1/2with ?1/(1+t) dt with a = 0, b = 1, and repeat the four steps. a. integrate using a graphing utility b. integrate exactly c. integrate by replacing the

  1. Calculus

    I have to use integration by parts to integrate tan^-1 (1/x)dx. I'm not sure what to use as u or dv. We were taught to use uv-integral of (vdu) to do this.

  2. Math

    Evaluate the integral of x*ln(1+x) dx by first making a substitution and then using integration by parts. I let u=1+x and du = dx but then ln(u) du can't integrate to anything?

  3. Calc

    How do you solve ∫sin(3x+4)dx? I got the -cos(3x+4) part, but do you have to integrate the 3x+4 too? Does chain rule apply?

  4. calculus help

    integrate cos^10xdx.. .plz show working i really wanna learn these thanks anyway

You can view more similar questions or ask a new question.