Hi people!

I can't solve these ones, they're tough!

Solve

Evaluate

Thanks!

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- Dec 17th 2007, 07:09 AMMessIntegrals!
Hi people!

I can't solve these ones, they're tough!

Solve

Evaluate

Thanks! - Dec 17th 2007, 07:19 AMbobak
for the second one do integration by parts, you should get an answer of

- Dec 17th 2007, 07:44 AMTKHunny
The definition of "tough" always has eluded me.

**Frequent Definition**: I don't know how to do it.

**Occasional Definition**: I can do it, but it takes too long and requires too much effort.

**Pratical Definition**: It can be done, but who would want to?

**Reasonable Definition**: I could spend a lot of time on this, using some way that I have concocted, but even if it works, there simply MUST be an easier way.

This leads me to ask two things:

1) Why have you been given these integrals? Are you REALLY expected to solve them in a closed form? Without a very specific hint, and with your missing he Integration by Parts on the second, it seems to me that the first is not reasonable. Do you have a specific hint?

2) Does one get to use numerical methods? Numbers are not evil. It's okay if that's what we have. - Dec 17th 2007, 08:20 AMcolby2152
- Dec 17th 2007, 08:48 AMKrizalid
Here's a specific calculation in this case.

So,

The rest is routine, and the answer is

Even I'd like to take a more general case:

Let

Define

Make substitution which can be written as the integral becomes

Define another substitution according to

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As for the first integral, set - Dec 17th 2007, 09:33 AMThePerfectHacker
- Dec 17th 2007, 10:12 AMKrizalid
Aha, yes! It's really cool! :D

- Dec 17th 2007, 10:24 AMcolby2152
- Dec 17th 2007, 02:08 PMmr fantastic
- Dec 17th 2007, 02:43 PMKrizalid
I wouldn't trust in the integrator, after substitution leads another integral which can be solved easily.

- Dec 18th 2007, 07:16 PMtopsquark
- Dec 18th 2007, 07:17 PMThePerfectHacker