Question

Solve:
$\int \frac{1-{\tan }^{2}x}{1+{\tan }^{2}x}dx$

Answer 1

$\int \frac{1-{\tan }^{2}x}{1+{\tan }^{2}x}dx$

$=\int \cos 2xdx$ [ Since $\cos 2x=\frac{1-{\tan }^{2}x}{1+{\tan }^{2}x}]$

$=\frac{\sin 2x}{2}+c$ [ Where $c$ is integrating constant]