Question

How do you find the integral of `f(x)=3x e^(-3x)` using integration by parts?

Answer 1

There are two things to try.

Explanation:

For integration by parts, we need two factors in the integrand.

In `int3xe^(-3x)dx = 3intxe^(-3x)dx` we already see two factors.

We begin by attempting the simplest approach:

Either integrate `x` and differentiate `e^(-3x)`

or differentiate `x` and integrate `e^(-3x)`.

Try them both to see the difference.

Using `u`, `dv` notation

Try using `dv=x dx` and `u=e^(-3x)`,

then try `u=x` and `dv=e^(-3x) dx`.