Posted by Hannah on Friday, February 13, 2009 at 1:49am.
How do you integrate [(x^2)(cos(2(x^3)))]? I tried to integrate by parts but I'm going in circles yet again...

Calculus  drwls, Friday, February 13, 2009 at 1:56am
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)]

Calculus  Reiny, Friday, February 13, 2009 at 8:03am
Wouldn't it simply be
(1/6)sin(2x^3) + c ?

Calculus  drwls, Friday, February 13, 2009 at 8:39am
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.
Answer This Question
Related Questions
 calculus  1) Integrate Cos^n(x) dx 2) Integrate e^(ax)Sinbx dx 3) Integrate (...
 Integral calculus  Please do help solve the followings 1) Integrate e^4 dx 2) ...
 [Calculus] Usubstitution for Integrals  Integrate from 1 to 5 of (3x5)^5 dx...
 Calc 1  integrate from 0 to pi/4 (sec^2x)/((1+7tanx)^2)^1/3 integrate form pi^2...
 Integral calculus  Please can anyone help with the following problems  thanks...
 Calculus  6.] Replace the integral in exercise 5 (int. (1/ 1 – t) dt a = 0, b...
 calculus 2  Justify, with a written explanation or a mathematical reasoning and...
 integrate  integrate du/3u and integrate x/x^2 dx it might be simple...i just ...
 PLZ integrate  integrate cos^3x dx tnk U
 Calculus AB  Please help me integrate this equation using partial fractions: ...
More Related Questions