For first one you don't need to integrate by parts. Simply sub
For the second one, you can either integrate by parts twice and treat the integral as the unknown or you can use the product to sum identity:
I have two problems I don't really know how to work through.
The first is the integral from 0 to 1 of r^3/(sqr(4+r^2))
I started by integrating by parts and eventually ended up with (4+r^2)^(7/2) so I know I'm doing something wrong.
The other problem is: find the integral of cosPIx * cos4PIx
I don't know where to begin here. Any help would be appreciated.
For the second one, I get to the integral of 1/2((cosPIx*cos4PIx + sinPIx*sin4PIx) + (cosPIx*cos4PIx - sinPIx*sin4PIx))dx
I'm pretty sure I use substitution but I don't know what I substitute. Am I allowed to set u=cosPIx du=-PIsinPIx and putting a 4 in front of u for the cos4PIx?