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September 3rd, 2017, 11:36 AM   #1
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integration

integrate 1/(4sin^2x-cos2x)
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September 4th, 2017, 07:44 AM   #2
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$\cos (2x)$ or $\cos^2 (x)$?

What have you tried?
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September 5th, 2017, 11:27 AM   #3
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we need cos2x
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September 5th, 2017, 11:47 AM   #4
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I would try $\cos{(2x)}=1-2\sin^2{(x)}$ and a Weierstrauß substitution, $t=\tan{(\frac{x}{2})}$.
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September 5th, 2017, 12:34 PM   #5
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Hint: $\dfrac{1}{4\sin^2(x) - \cos(2x)} = {\small\dfrac12}\sec^2(x) \left(\dfrac{1}{\sqrt5\tan(x) - 1} - \dfrac{1}{\sqrt5\tan(x)+ 1}\right)$.
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