From

d(fg) = fdg + gdf

upon integrating both sides and rearranging, we get

Use of this statement is called "integration by parts".

It is useful when the integral on the right is recognizable, or is a multiple of that on the left.

These occur when the integrand is a monomial times an exponent or trigonometric function, or when the integrand has logarithms in it. It can often be used when the integrand has other inverse functions in it, as well.

It also helps for inverse powers of sine and cosine.