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] U-substitution for Integrals - Integrate from 1 to 5 of (3x-5)^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 ...
- 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