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# Integration watch

1. Hi,

How the hell do I integrate

???

I though about setting u=lnx so it's the integral of u^n x e^u du, but I can't do the parts bit afterwards

Cheers!
2. I can't really tell from that whether or not mine was right Maple agrees with me but I don't really trust it
3. (Original post by vector)
I can't really tell from that whether or not mine was right Maple agrees with me but I don't really trust it
You are right (ignoring +C )
4. Cool, cheers
5. Question changed
6. Looks like a reduction formula question to me. Try doing parts with u=(lnx)^n, dv/dx = 1 and go nuts like you'd go nuts on ya **** around a purdy ladee.

When you do this, setting your integral equal to I_n you get:

EDIT: Okay, so this requires you to be able to solve a first oder difference equation. I'm rusty with these badboys. I'll check it's do-able,

EDIT 2: Yes. I'll spoilerise the method to solve the difference equation you get, for if you fancy having an atack yourself

Spoiler:
Show
Multiply the equation through by 1/n!, and set . Then you'll have . From here you can (hopefully) easily work out what S_n is, and thus what I_n is

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