Integrate by Parts: Solving x^13cos(x^7)dx

[punjabi_monster]

Integration by parts :(

hi I have been trying this question for quite a while now and am unsure of what to do. Any help would be apprectiated.

Integral x^13 cos(x^7) dx

I know you have to use integration of parts. Here is what i have done so far:

let U=x^3
dU =13x^12 dx

dV=cos(x^7)
V=?
First off I can't manage to find the antiderivative of cos(x^7)

After finding that i think you use
integral u(dV) = uv - v(dU)

 

[Signifier]

Rewrite the integral as (x^7 * x^6) * cos (x^7). Then let u = x^7. Then du = 7x^6 dx. So the integral becomes:

(1/7) § u cos(u) du

Which you can integrate by parts. Then substitute u back in and you're done.