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- Feb 17th 2008, 05:32 PMpolymeraseMore integrals

Thanks - Feb 17th 2008, 06:28 PMangel.white
IDK if this is the best way to get the answer, but it's how I found it. Fist, cos2x = cos^2x-sin^2x so

multiply by

Mess with the denominator:

And now we can use these rules:

Simplify

Simplify

Make substitution

Distribute the 2 into the denominator

Integrate

Anti-substitute

I'm pretty sure that's right, at the very least, I like all the steps I used to get there. - Feb 17th 2008, 08:13 PMSoroban
Hello, polymerase!

This is a shorter version of angel.white's solution . . .

Quote:

Multiply by

Let

Substitute: .

Back-substitute: .

- Feb 17th 2008, 08:56 PMangel.white
- Feb 18th 2008, 05:07 AMKrizalid
Fast solutions always are found with practice and of course, experience. (Smart people can get fast solutions too.)

- Feb 18th 2008, 11:42 AMSoroban
I just tripped over the most amazing approach . . .

Quote:

Multiply by

Let

. . Then: .

Substitute: .

Back-substitute: . . . . ta-*DAA!*

Is that scary enough?

- Feb 18th 2008, 11:44 AMJhevon
- Feb 18th 2008, 01:24 PMangel.white
Gonna have to check for it under my bed tonight with a flashlight. (Sweating)

- Feb 18th 2008, 02:03 PMKrizalid
Well anyway to contemplate it wasn't necessary to apply the product rule, just note and the rest follows.

- Feb 18th 2008, 02:21 PMJhevon