- #1

- 3

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Actually, universal substitution does make it possible to integrate, but there has to be some shorter, more elegant way. Anyone?

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- Thread starter reaper616
- Start date

- #1

- 3

- 0

Actually, universal substitution does make it possible to integrate, but there has to be some shorter, more elegant way. Anyone?

- #2

- 1,838

- 7

- #3

- 3

- 0

I'm sorry, but I'm not sure that I understand what are you trying to say. Could you go a little bit more in-depth?

- #4

- 1,838

- 7

[S^2 + C^2]/[S (2 C^2 - 1)] =

S/[2 C^2 - 1] (easy to integrate as the derivative of C is -S and S is in the numerator)

+

C^2/[S(2C^2 - 1)]

We can rewrite the numerator of the last term as:

C^2 = 1/2 2 C^2 = 1/2 (2 C^2 - 1 + 1)

This means that you can write the last term as:

1/(2S) + 1/2 * Original term you wanted to integrate.

Then you're done if you can integrate 1/S and that you can do using more or less the same trick:

1/Sin(x) = 1/(2Sin(1/2 x) Cos(1/2 x)) and then replace the numerator by Cos^2(1/2 x) + Sin^2(1/2 x) and you're done.

- #5

- 3

- 0

It works. Very nice. Thank you very much.

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