Question

How do you know to use integration by parts?

Answer 1

Since the integration by parts is essentially the product rule for integration, an integral whose integrand is the product of functions is most likely to call for the integration by parts.

Let us look at a simple example.

`int xe^xdx`

As you can see, the integrand is the product of `x` and `e^x`, so the integration by parts is a good one to try.

Let `u=x` and `dv=e^xdx`,
`Rightarrow du=dx` and `v=e^x`

By Integration by Parts: `int udv=uv-intvdu`,

`=xe^x-int e^xdx`

By Exponential Rule,

`=xe^x-e^x+C`