We may encounter the integral

and none of the techniques learnt so far seems to work. But here the derivative of a product of functions will be very useful:

which is nearly what we need! Indeed

Great! This technique is called integration by parts and works as follows: let $u(x)$ and $v(x)$ be some functions. We know that

so if our integrand is of the form $uv'$, we may switch to a completely different, and perhaps simpler, integral: