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  4. y = ∫ cos 2tan-1 √(1-x/1+x) dx is an equation of a family of

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Q. $y = \int cos \left\{2tan^{-1} \sqrt{\frac{1-x}{1+x}}\right\} dx$ is an equation of a family of

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Solution:

Putting $x = cos2 \theta \, \therefore \,cos \left\{2tan^{-1} \sqrt{\frac{1-x}{1+x}}\right\} = cos2\theta = x$
$\therefore \,y = \int xdx = \frac{x^{2}}{2}+c$