Find

It seems pretty trivial, but find a quick solution.

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- May 9th 2008, 04:51 PMKrizalidToday's calculation of integral #15
Find

It seems pretty trivial, but find a quick solution. - May 9th 2008, 04:57 PMMathstud28
- May 9th 2008, 04:58 PMKrizalid
That's not a quick solution, you omitted details that you should explain at least.

- May 9th 2008, 05:20 PMMathstud28
Ok I owe it at least that much...

Now using integration by parts on the second and standard techniques on the first we obtain the antiderivative

O...and just because I know you love it

Integrating we get

(Itwasntme)

That was obviously a stupid joke^...me attempting to be funny - May 9th 2008, 05:27 PMKrizalid
Partial integration is involved. Find another solution which does not involve integration by parts.

- May 9th 2008, 05:46 PMPaulRS
Let:

Then:

Summing the expressions above :

And:

Thus: - May 9th 2008, 05:58 PMKrizalid
Pretty similar I did. I defined

- May 9th 2008, 07:46 PMJhevon
I got confused with the method shown. here's another:

note that

Thus,

- May 10th 2008, 01:51 AMflyingsquirrel
- May 10th 2008, 02:59 AMPaulRS
- May 10th 2008, 07:15 AMKrizalid
Here's my solution:

Let Substitute In general hence