Evaluate the integral of

Question

xe^2x(dx)

A. (1/6)(x^2)(e^3x)+C

B. (1/2)(xe^2x)-(1/2)(e^2x)+C

C. (1/2)(xe^2x)-(1/4)(e^2x)+C

D. (1/2)(x^2)-(1/8)(e^4x)+C

Answer 1

u dv = u v - int v du

u = x
du = dx

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

= (x/2)e^(2x)- (1/4)e^(2x) +c
so I think C.