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August 6th, 2016, 05:52 AM   #1
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Indefinite Integration

$\displaystyle \int\frac{\sin (x+\alpha)}{\cos^2 x}\sqrt{\frac{\csc x+\sec x}{\csc x-\sec x}}dx$
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August 6th, 2016, 06:32 AM   #2
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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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