# Integration by parts.

• Apr 20th 2009, 12:31 PM
gammaman
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?

$\int{x^5sin(x^3)}$
• Apr 20th 2009, 12:37 PM
TheEmptySet
Quote:

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
• Apr 20th 2009, 12:45 PM
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.
• Apr 20th 2009, 12:48 PM
TheEmptySet
Quote:

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.

(Wink)