integration?

Question

find the integral of x^3 * e^(2x) dx.

Answer 1

Using repeated integration by parts I get
(e^2x)(4x^3 - 6x² + 6x -3)/8 + C

Doug

Answer 2

integral of x^3 * e^(2x) dx.
u=x^3 du=3x^2 dx dv=e^(2x)dx v=1/2 *e^2x
uv-integral(vdu)
x^3*1/2*e^2x-integral(1/2e^2x*3x^2dx)
1/2(x^3*e^2x)-3/2*integral(e^2x*x^2dx)
u=x^2 du=2x dv=e^2x v=1/2e^2x
1/2(x^3*e^2x)-3/2[(1/2)*x^2*e^2x-integral(1/2e^2x*2xdx)]
u=2x du=2dx dv=1/2e^2x v=1/4e^2x
1/2(x^3*e^2x)-3/2[(1/2)*x^2*e^2x-[2x*1/4e^2x-integral(1/4e^2x*2dx)]
1/2(x^3*e^2x)-3/2[(1/2)*x^2*e^2x-[2x*1/4e^2x-1/4e^2x]]
1/2(x^3*e^2x)-3/2[e^2x(1/2x^2-1/2x-1/4)]
1/2(x^3*e^2x)-3/2[e^2x(1/2x-1/2)^2]
e^2x[1/2x^3-3/2(1/2x-1/2)^2]

Answer 3

3x+2xe