1. ## Integration by parts.

I know this integral is an integration by parts, but what is the correct approach to breaking it up so that it becomes solvable?

$\int{x^5sin(x^3)}$

2. Originally Posted by gammaman
I know this integral is an integration by parts, but what is the correct approach to breaking it up so that it becomes solvable?

$\int{x^5sin(x^3)}$
$u=x^3 \implies du=3x^2dx$ and

$dv=x^2\sin(x^3)dx \implies v=-\frac{1}{3}\cos(x^3)$

You should be able to finish from here

3. Thanks, but according to my notes

u=1/3x^3
du=x^2
dv=3x^2sin(x^3)
v=-cos(x^3)

does this make sense? Your way seems much more logical.

4. Originally Posted by gammaman
Thanks, but according to my notes

u=1/3x^3
du=x^2
dv=3x^2sin(x^3)
v=-cos(x^3)

does this make sense? Your way seems much more logical.
You will get the same answer either way. If you write them out you will see that they are equivilent.