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How to integrate $$\frac{\sec^2 x}{({\sec x+\tan x})^{9/2}}$$ with respect to $x$. I tried to express the denominator in the form of half angles but i could not succeed

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Always try to write your question in Latex. Is this what you meant? – Samrat Mukhopadhyay Jul 24 '13 at 17:51
Yes that's what I really meant. :) – Prahlad Jul 24 '13 at 17:54

Big Hint:

Use the substitution $u=\sec x+\tan x$, and notice that $\frac{1+u^2}{2u}=\sec x$.

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