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
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.
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.
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:
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.