Question

find the integral

~(e^x + x)^2 (e^x + 1)dx


can you pls explain how it arrive to this?

ans = 2e^4x + C

Answer 1

integral( (e^x+ x)^2 * (e^x + 1) dx )

let u = e^x + x
du = (e^x + 1)dx

Now you have integral(u^2 du)
= (u^3)/3 +C
= ((e^x + x)^3)/3 +C
= (e^3x + 3x*e^2x + 3x^2*e^x + x^3)/3 +C

Are you looking at the right answer key?