1. ## Integration by parts

Hi, I just learned integration by parts. I'm trying to solve:
$\int x^2 sin(3x+1)dx\$
I know usually you want u to have the simpler derivative.
I set u=sin(3x+1), du=3cos(3x+1), v=(1/3)x^3, dv=x^2

So using integration by parts, uv- integral vdu
$sin(3x+1)(1/3)x^3 - \int (1/3)x^3 3cos(3x+1)$

then I went through the steps to get my final answer:
$(1/3)x^3sin(3x+1)-(1/12)x^4sin(3x+1) +C$

2. Originally Posted by bcahmel
Hi, I just learned integration by parts. I'm trying to solve:
$\int x^2 sin(3x+1)dx\$
I know usually you want u to have the simpler derivative.
I set u=sin(3x+1), du=3cos(3x+1), v=(1/3)x^3, dv=x^2

So using integration by parts, uv- integral vdu
$sin(3x+1)(1/3)x^3 - \int (1/3)x^3 3cos(3x+1)$

then I went through the steps to get my final answer:
$(1/3)x^3sin(3x+1)-(1/12)x^4sin(3x+1) +C$

$u = x^2$
$dv = \sin(3x+1) \, dx$