Question
Evaluate the following integrals:
$\int\frac{1}{\sqrt{\tan^{-1}\text{x}}.(1+\text{x}^2)}\text{dx}$
$\int\frac{1}{\sqrt{\tan^{-1}\text{x}}.(1+\text{x}^2)}\text{dx}$
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$\log \left[\tan ^3 x \cdot \sin ^4 x \cdot\left(x^2+7\right)^7\right]$
$x=\cos ^{-1}\left(\frac{2 t}{1+t^2}\right), y=\sec ^{-1}\left(\sqrt{1+t^2}\right)$