Note that , where (this is of course the old trick).
Note that and therefore , where c is a constant (this is an interesting result). To get c, use the well known result for .
Therefore: and so .....
No. (And let's not get into infinite recursion here).
Nor is anyone. Which would make for a pretty boring board.
Out of interest, why are you posting these integrals? Are they red rags being waved at bulls? My speculation is that at this time of year business is slow and questions like these liven things up a bit (and have good teaching points as well).
Krizalid, you have a good reputation here. And sometimes you solve the problem yourself immediately after the question. That confuses me
Do you want someone to solve them OR do you want it to be some kind of a tutorial ? If it's the latter you could probably post it under Calculus Tutorials. Ask TPH or someone else to choose your integrals as the Problem of the Week e.t.c. Or at least specify it while posting.
Now if it is the former, you probably want someone to solve it in a different way(Given the fact that you always know the solution). If so, then I suggest you specify the methods you have tried. This will stop causing confusions.No poster(helpers I mean) would want their time to be wasted,right?
Naturally , I am sure, all of us appreciate a good mathematical discussion. So I request you to be clear so that we can have a healthy "integration" debate and not quarreling in such a nice forum.
Hope you understand what I mean
I'm just posting problems like proposed ones.
I hope I've clarified doubts about integrals
P.S.: in fact, discussion's title is related to the solution that I'm lookin' for.