Chapter 9.5, Problem 1CYU

The integral formula ${\displaystyle \int \left(at+b\right)e^{-rt}dt}=e^{-rt}\left[\frac{-1}{r}\left(at+b\right)-\frac{a}{r^2}\right]+C\left(r\ne 0\right)$ is used in many applications in this section. Derive it using integration by parts.