# Thread: [SOLVED] Integration by parts

1. ## [SOLVED] Integration by parts

This is a problem I am having trouble with:
$
\int 5xcos(5x) dx
$

This is the formula we were taught in class to use for these types of problems:
$
\int udv = uv - \int vdu
$

I came up with this but I am sure it's wrong.
$
xsin(5x) - \int sin(5x)
$

2. Originally Posted by redman223
This is a problem I am having trouble with:
$
\int 5xcos(5x) dx
$

This is the formula we were taught in class to use for these types of problems:
$
\int udv = uv - \int vdu
$

I came up with this but I am sure it's wrong.
$
sin(5x) - \int xsin(5x)
$
yes, it's incorrect. did you identify your u and dv? show your steps so we see where you went wrong.

3. I set u=5x du=5 dv=cos(5x) and v=1/5 sin(5x)

That gave me:
$
xsin(5x) - \int sin(5x)
$

I tried to use -1/5x cos(5x) for the part in the integral but it is still wrong.

4. Originally Posted by redman223
I set u=5x du=5 dv=cos(5x) and v=1/5 sin(5x)

That gave me:
$
xsin(5x) - \int sin(5x)~{\color{red}dx}
$

I tried to use -1/5x cos(5x) for the part in the integral but it is still wrong.
that is correct. all you need to do now is find $\int \sin 5x~dx$ and wrap it up

5. Thanks, for some reason I kept thinking that the derivative of 5x was 5x and not 5, lol.

I came up with -1/5 cos(5x) and it was correct. Thanks.