# Math Help - Integral problem

1. ## Integral problem

I'm trying to figure out the integral of (x^3)(sin x). Any pointers?

2. This one requires integration by parts three times.

For start, set $u=x^3$ & $dv=\sin x\,dx.$

3. Originally Posted by taichu
I'm trying to figure out the integral of (x^3)(sin x). Any pointers?
are you allowed to use Integration by parts? i.e,
$\int udv = uv - \int vdu$

if so, do it three times..

4. Haha, I just figured that out now, and came to post my solution.

What I got was -x^2 cos x + 3x^2 sin x - 6x cos x + 6 sin x + C.

5. Originally Posted by taichu
Haha, I just figured that out now, and came to post my solution.

What I got was -x^2 cos x + 3x^2 sin x - 6x cos x + 6 sin x + C.
that is incorrect, i believe

check the answer here

6. Originally Posted by taichu
Haha, I just figured that out now, and came to post my solution.

What I got was -x^2 cos x + 3x^2 sin x - 6x cos x + 6 sin x + C.
it should be
$x^3 \cos x + 3x^2 \sin x - 6x \cos x + 6 \sin x + C$