Integration by parts
posted by Steff on .
integrate (e^xx)^2 dx

I would expand it first
∫ (e^x  x)^2 dx
= ∫ e^(2x)  2xe^x + x^2 dx
let's concentrate on the middle term, since the other two terms are easy to integrate
∫ 2xe^x dx
let u = 2x , let dv = e^x dx
du = 2dx and v = e^x
then ∫ 2xe^x dx = (2x)(e^x)  ∫ 2e^x dx
= 2xe^x  2e^x
finally ...
∫ (e^xx)^2 dx
= ∫ e^(2x)  2xe^x + x^2 dx
= (1/2e^(2x)  (2xe^x  2e^x) + (1/3)x^3 + c
= (1/2)e^(2x)  2xe^x + 2e^x + (1/3)x^3 + c