Chapter 2.11, Problem 17P

Evaluate ${\displaystyle \int \frac{e^{ax}(a\cos bx+b\sin bx)}{a^2+b^2}}$ and take real imaginary parts to show that:

${\displaystyle \int e^{ax}\cos bxdx=\frac{e^{ax}(a\cos bx+b\sin bx)}{a^2+b^2}}$