\[\integral\_{}^{}{\frac{\sec^{2}x}{(1 + \tan x)(2 + \tan x)... | MATH - INTEGRATION BY SUBSTITUTION | SolveeIt

$\int_{}^{}{\frac{\sec^{2}x}{(1 + \tan x)(2 + \tan x)}\mspace{6mu} dx}$

$1 + \tan x = t$

$2 + \tan x = t$

$\tan x = t$

$\int_{}^{}{\frac{\text{cose}\text{c}^{2}x}{1 + \cot x}dx =}$

Answer

$2 + \tan x = t$

Explanation

Put $\text{cosec}x - \sin x + c$ then

${logtan}x + c$ .

Question: \[\int_{}^{}{\frac{\sec^{2}x}{(1 + \tan x)(2 + \tan x)}\mspace{6mu} dx}\]...