Question

Evaluate $\int \frac{se{c}^{2}x}{3+ta{n}^{2}x}dx$

Answer 1

$I=\int \frac{se{c}^{2}x}{3+ta{n}^{2}x}dx$

Put $\tan x=t$

$se{c}^{2}xdx=dt$

$I=\int \frac{dt}{3+t^2}dt$

$I=\int \frac{dt}{(\sqrt{3}{)}^2+t^2}$

$I=\frac{1}{\sqrt{3}}ta{n}^{-1}\left(\frac{t}{\sqrt{3}}\right)+C$

$I=\frac{1}{\sqrt{3}}ta{n}^{-1}\left(\frac{\tan x}{\sqrt{3}}\right)+C$