integral((1-cos^4 x)/(cot x-tan x))

in this i have taken 1 as (sin^2 x+cos^2 x)^2

what should i do after that

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- Jun 5th 2011, 12:53 AM #1

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- Jun 5th 2011, 02:43 AM #2

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One way I guess would be to set t=tan x, so you get an integral of a rational expression. Then you would have to solve the resulting integral with partial fractions.

By setting t=tan x I get

The rest of it is evaluating this integral. To begin with you should substitute for u=t^2. And so on. Hope this helps a little, and also hope someone has a more elegant solution.

EDIT:

Sorry, that way would have been hard, here is a better one. Note that:

So if you use that and substitute you should be able to solve the integral np.

- Jun 5th 2011, 03:34 AM #3

- Jun 5th 2011, 04:15 AM #4

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- Jun 5th 2011, 09:13 AM #5

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- Jun 5th 2011, 09:19 AM #6

- Jun 5th 2011, 09:26 AM #7

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- Jun 5th 2011, 09:39 AM #8

- Jun 5th 2011, 09:56 AM #9

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Hm, sorry for interrupting if you didn't like my solution, but since this is my first post I'd still like for it to be helpful.

As mentioned, using the fact that:

you can rewrite the denominator as:

.

So with the other substitute for the cosine, you get:

Rewriting:

So the main idea is that the sine disappears with the substitution

So returning to the integral:

Which should prove a fairly easy integral.

Well, anyway... if you're going the other way still consider substituting at least . Good luck.