# Math Help - integration by parts

1. ## integration by parts

I am trying to do this:
integral sign xsec^2(3x)dx
I am stuck on how to do it help plz. How do you do these types of problems?

2. Hello, davecs77!

$\int x\sec^2(3x)\,dx$

By parts: . $\begin{array}{ccccccc}u & = & x & \quad & dv & = & \sec^2(3x)\,dx \\ du & = & dx & \quad & v & = & \frac{1}{3}\tan(3x)\end{array}$

Then: . $\frac{1}{3}x\tan(3x) - \frac{1}{3}\int\tan(3x)\,dx \;=\;\frac{1}{3}x\tan(3x) + \frac{1}{9}\ln\left|\cos(3x)\right| + C$