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Integrate : ( square root (cos x /x ) - square root (x /cos x) sin x )
Solution:

$I=int (sqrtfraccos xx-sqrtfracxcos xcdot sin x)dx$

$\ \ I= int fraccos x -x sin xsqrtx cos xdx$ Put $x cos x= t^2$

$Rightarrow$ $(cos x-xsin x)dx=2tdt$

$\ \ Rightarrow I=int frac2ttdt=2t+c=2sqrtxcos x+c.$

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