Thread: Integration by parts

I went wrong somewhere here. First let's say:


Let's integrate that by parts. Let's start with:





Next:



Let's integrate by parts again on that new integral because I think I can get back to the original integral:






So we have:



All together:


I don't think I did it right because the my next step appears to be a dead end:


I did something wrong with the coefficients or the signs methinks... or everything. That's always a possibility with me.

Originally Posted by jamesrb

I don't think I did it right because the my next step appears to be a dead end:

/edited.

so while you were right in your process, this yielded no information. Let and instead for your second integral.

Originally Posted by MacstersUndead

/edited.

so while you were right in your process, this yielded no information. Let and instead for your second integral.

Alright so if I do that I get:



Can I pull a -1 out of [tex](-sin(x))[/text]? To get:


So all together:




Finally:


My calculus book says the answer is:


I think those are equivalent answers.

They are equivalent answers. Well done.