Question

@Yttrium Integration by parts.
\[\int e^x x dx\]

Answer 1

Can you do it first?

Answer 2

Sure.

Answer 3

\[(e^x)x - e^x\]
Is the answer
\[e^x (x-1)\]

Answer 4

Don't mind if I'm wrong I just applied the mibp.

Answer 5

Hmm, it is right....
How about \[\int xsinx dx\]

Answer 6

\[sinx - xcosx \]

Answer 7

Hmmm, if you can do these questions, what's your problem then?

Answer 8

I want the shortcut. I want to solve faster.

Answer 9

I need the MIBP technique but I can't find it.

Answer 10

What kind of shortcut?

Answer 11

It is called Multiple Integration by Parts.

Answer 12

I don't understand what do you mean by multiple integration by parts...
\[\int udv =uv-\int vdu\]is the one is usually use, but it is the same as \[\int uv'dx =uv-\int vu'dx\]
Hmm... As for "shortcut", one of those might be \[\int e^x(f(x) + f'(x)) dx = e^xf(x)+C\]