intergrate by parts, : xe^(2x) dx?

Question

need help in this question...
intergrate by parts not by substitution..
thankyou

Answer 1

let u= x , du = dx

dv = e^(2x)dx v = 1/2 e^(2x)

I = 1/2 x*e^(2x) - integral(1/2 e^(2x) dx) = 1/2 x e^(2x) -1/4 e^(2x)

I = 1/2 e^(2x)*{ x - 1/2}