Posted by **J** on Sunday, February 22, 2009 at 9:37pm.

How do I evaluate this integral: x^9cos(x^5)dx

Hint: First make a substitution and then use integration by parts.

- Calculus -
**drwls**, Monday, February 23, 2009 at 2:31am
If w = x^5, 5x^4 dx = dw

The integral you want becomes the integral of

(1/5) w cos w dw

Now use integration by parts, with

u = w dv = cosw dw

du = dw v = sin w

The integral becomes

(1/5)[u v - Integral v du]

= (1/5)[w sin w - integral of sin w dw]

= (1/5)[w sin w + cos w]

= (1/5) [x^5 sin(x^5) + cos(x^5)]

Check my work. The method seems correct by my algebra is often sloppy.

## Answer This Question

## Related Questions

- Calculus - First make a substitution and then use integration by parts to ...
- Calculus - First make a substitution and then use integration by parts to ...
- Calculus - First make a substitution and then use integration by parts to ...
- Calculus - Use either substitution or integration by parts to evaluate the ...
- Calculus Please Help2 - Evaluate the integral by using substitution. Use an ...
- Calculus - Use integration by parts to evaluate the integral xsqrt(2x+6)dx.
- Math/Calculus - How would I integrate the following by parts: Integral of: (x^2...
- Calculus - Use integration by parts to evaluate the definite integral. S 12 x/...
- calc - evaluate the integral: y lny dy i know it's integration by parts but i ...
- calculus - how to take the integral of cos(square root of x) dx. need to use ...

More Related Questions