Originally Posted by

**synclastica_86** I need to do an integral for my quantum mechanics homework but it has been a while since I've taken calc so my math is a bit rusty.

$\displaystyle \frac{4}{L^2}\int^L_0\sin^2(\frac{m\pi x_2}{L})\int^L_0x_1^2\sin^2(\frac{n\pi x_1}{L})dx_1dx_2$$\displaystyle =\frac{4}{L^2}\int^L_0\sin^2(\frac{m\pi x_2}{L})dx_2\int^L_0x_1^2\sin^2(\frac{n\pi x_1}{L})dx_1$

The first integral I can do, it's the second one that I'm having trouble with. I tried by parts and know that I can do it with brute force, but the it involves using by parts multiple times. In physics, we are usually given less involve math problems, so I was just wondering whether there is a more elegant way to do this.