Question

1) evaluate

integral of xe^3x dx

2) evaluate integral form 1 to 0 of 4e^2x dx

I just need help finding the anitderivative. Would it be 2e^2x?

Answer 1

u = 3x
dx = (1/3) du

(1/3) u e^u * (1/3) du
= (1/9) u e^u du

= (1/9) [ ue^u - e^u]

= (1/9) [ 3x e^(3x) - e^(3x) ]

Answer 2

d/dx ( 2e^(2x) ) = 4 e^(2x) so yes

Answer 3

for number 2 how did you get 2e^2x?