integral(sinte^(6/489)(t))

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- Jan 29th 2009, 07:18 AMlord12how do i find this integral?
integral(sinte^(6/489)(t))

- Jan 29th 2009, 07:30 AMlord12
I know that I cannot use integration by parts since it always loops.

- Jan 29th 2009, 07:46 AMChris L T521
Is this your integral: ??

If so you can use integration by parts. The key to this one is that you apply integration by parts**twice**. After you apply it twice, you'll see the original integral reappear.

I.e. you'll see after applying IBP twice that you will end up with

Then you treat as a variable and then solve for it.

Does this make sense? - Jan 29th 2009, 08:50 AMSoroban
Hello, lord12!

Yes, it "loops" when doing it by-parts, but that's what we want!

Quote:

. Why did they use such an ugly fraction?

We have: .

. . By parts: .

And we have: .

. . By parts: .

And we have: .

. . . . . . . . . .

We have: .

Factor: .

Then: .

Therefore: .

- Jan 29th 2009, 09:12 AMheathrowjohnny