Howdy,

So, i have a question about partial integration.

Acctually this question concerns Integration in general.

How do you know how to choose the variables for substitution?

For example i have $\displaystyle \int x^2 cos(\pi x) dx$

If we pick U =$\displaystyle x^2$ and V = $\displaystyle -\frac{1}{\pi}*sin(\pi x)$

dU = $\displaystyle 2x$ and dV = $\displaystyle cos(\pi x)$

so...

$\displaystyle UV -\int V*dU$

= $\displaystyle \frac{1}{\pi}sin(\pi x) * x^2 -\int 2x * -\frac{1}{\pi}sin(\pi x)$

...

This is the point where i start to doubt wether i've choosen the right variables for substitution.