find the integral
~(e^x + x)^2 (e^x + 1)dx
can you pls explain how it arrive to this?
ans = 2e^4x + C
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?