September 3rd, 2017, 11:36 AM  #1 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  integration
integrate 1/(4sin^2xcos2x)

September 4th, 2017, 07:44 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,146 Thanks: 2386 Math Focus: Mainly analysis and algebra 
$\cos (2x)$ or $\cos^2 (x)$? What have you tried? 
September 5th, 2017, 11:27 AM  #3 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8 
we need cos2x

September 5th, 2017, 11:47 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,146 Thanks: 2386 Math Focus: Mainly analysis and algebra 
I would try $\cos{(2x)}=12\sin^2{(x)}$ and a WeierstrauÃŸ substitution, $t=\tan{(\frac{x}{2})}$.

September 5th, 2017, 12:34 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,586 Thanks: 1489 
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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