How to integrate $\int\frac{\sin(kx)}{e^x}dx?$

Question

How would one integrate $$\int\sin(kx)e^{-x}dx, k\in\mathbb{R}?$$ I have tried integration by parts $$\int\sin(kx)e^{-x}dx=$$

Answer 1

Hint

$$\int\frac{\sin(kx)}{e^x}dx=Im\left(\int e^{-x+ikx}dx\right)$$