Substitution Exponential Functions Indefinite Integrals

Question

∫(e^x+1)(e^x+x)^4

Please explain each step in detail. Thank you!

Answer 1

Use u substitution:

u = e^x + x --> du/dx = e^x + x --> dx = du/(e^x+1)

integral [u⁴ du]

u⁵/5 + C = (e^x + x)⁵/5 + C