Hey guys, I have this problem I have been trying to solve for the longest time.
Not looking for a complete solution, maybe part of one would be nice.
I'm trying to integrate
So far I have tried 2 ways of going at it.
First I completely expanded the integral
I have no problem integrating
I just simply use the substitution technique.
The next part gets tricky, I'm stumped. Any of the functions with x variables I simply can't seem to do.
I tried substituting by parts by either making or so on and so forth
I went to wolframalpha.com and tried to understand what they did step by step
For example, I tried to integrate just like the site did. They say to substitute and to get
Either I am feeling really dumb right now and the answer is right in from of me or the answer is completely wrong. How did wolframalpha manage to get
=
All help is greatly appreciated
The problem is in the red step and obviously the step that follows from it. You see you did . Which would be fine if that's what it was, but you see the factor is attached to a term, hence what you did does not make any sense. If you further factor out the and then do and carry forwards you will get the correct answer.
I'll do a step-by-step solution if you're having difficulty with the integral. Or just to give you something to compare your work to.
Let
Then, let , hence ie. .
Then Hence
Therefore
So by multiplying out we get , since we get
, which we can actually further factor to give where of course.