Question

integration : x(e^(3x)) dx

Answer 1

hi

Answer 2

i tried to use 'u' sub but it didn't work.

Answer 3

hmm

Answer 4

Use integration by parts.
\[u = x \\ dv = e^{3x} dx\]

Answer 5

it can't be used isn't it? since dv doesn't have 'x dx'

Answer 6

You don't need an x, just a dx. And you have one.

Answer 7

ok let me try it

Answer 8

I'll do \(\int x e^x dx\) for you as an example. Then you should see how to do it.
\[u = x \\ du = dx \\ dv = e^x dx \\ v = e^x\]
So plugging into \[uv - \int v du\] We get \[xe^x - \int e^x dx\]
Resulting in: \(xe^x - e^x + C\)