Have you considered using the binomial theorem/expansion? It wouldn't be too ugly ...
I have the following question that I'm having issues solving
I tried using uv substitution with u being and v being just dx. However, it quickly devolved into uv substitution after uv substition that spiralled into a massively negative number, so I must be doing something wrong. My plan was just to uv until I got that exponent down to something I could easily multiply out.
Any tips, tricks, or something I may have missed?
Thanks to you all for being of assistance. @theChaz, I was trying to avoid actually expanding that, though I suppose it's always an option.
@cheme and Prove It, looks like you two are advocating the same method, with Prove It's being a bit quicker and to the point. I'm afraid I'm not really following, though. I was wondering if you could clarify.
I understand taking the and setting is as u. Then .
From my understanding, this basically gets us down to , so I need to use the du definition above to replace the dx. But I get stuck here. Can someone show me the rest of the substitution part?
If I try to work through it, I end up with:
I can't just move the to the left side so I get a straight definition for dx.
Siron, thanks for the assistance. I'm probably missing something blindingly obvious, but how do you get from to ?
Once you substitute everything back into the integral, I follow the rest of it.
...jeez, what a mess. At any rate, assuming I didn't make a mistake somewhere along the line, you end up with a really ugly fraction.