August 6th, 2016, 06:52 AM  #1 
Senior Member Joined: Jul 2011 Posts: 399 Thanks: 15  Indefinite Integration
$\displaystyle \int\frac{\sin (x+\alpha)}{\cos^2 x}\sqrt{\frac{\csc x+\sec x}{\csc x\sec x}}dx$

August 6th, 2016, 07:32 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,145 Thanks: 2385 Math Focus: Mainly analysis and algebra 
I would start by expanding the $\sin(x+\alpha)$ using $\sin(A+B)=\sin A\cos B + \cos A \sin B$. Then, the Weierstrass substitution $t=\tan {x {over 2}$ will remove the trigonometric terms. Whether or not the square root also disappears I don't know.


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