Integration By Parts?

Question

Integral= (x)(e^3x)dx

Answer 1

u = x
and dv = (e^3x)dx

Try it.

Answer 2

int x(e^3x)
formula is int u dv=uv-int vdu-----1
here u= x dv=e^3x
du=dx v=1/3 e^3x
substituing in 1 we get
xe^3x=x 1/3e^3x-int 1/3e^3x dx
=x/3e^3x-1/3e^3x/3
=x/3e^3x-1/9e^3x
=1/3e^3x(x-1/3)

Answer 3

int (udv) = uv-int(vdu)
let u=x
let dv=e^3xdx
du=1dx
v=(1/3)e^3x

so...(x)[(1/3)e^3x] - int(vdu)
(1/3)(x)(e^3x) - (1/3)int(e^3x)dx
(1/3)(x)(e^3x) - (1/3)(1/3)(e^3x)

from there, simplify how you choose

Answer 4

I = ∫ x.e^(3x) dx
I = ∫ (u).(dv/dx).dx = uv - ∫ v.(du/dx).dx
Where u = x and dv/dx = e^(3x)
du/dx = 1 and v = (1/3).e^(3x)
I = (1/3).x.e^(3x) - (1/3).∫ e^(3x).dx
I = (1/3).x.e^(3x) - (1/9).e^(3x) + C
I = (1/9).e^(3x).(3x - 1) + C

Answer 5

the first post is correct.