integrate the following question

Question

integrate the following question :

∫ (e^y - y e^-y ) dy

Please write the answer with explanation steps

Answer 1

∫e^y dy = e^y

Integrate the 2nd term by parts

v = y

dv = dy

u = e^-y

du = -e^-y dy

and the integral is ye^-y + e^-y

Add these 2 parts and add a constant term for your answer.