Find the integral of xcos5x dx

[fk378]

Homework Statement

Find the integral of xcos5x dx

Homework Equations

uv- (integral)vdu

The Attempt at a Solution

I tried to pick u=cos5x and dv=xdx, but the book uses u=x, dv=cos5x dx

Why can't my way work?

 

[NateTG]

Why can't my way work?

It can. Generally, people choose the $u$ and $v$ so that the problem is simplified - the way the book chooses makes the integrand more tractable.