Question

$\int \frac{d_X}{{\sin }^{2}x+\sin 2x}=$

• A. $\frac{1}{2}\log |\frac{\tan x}{\tan x+2}|+c$
• B. $\frac{-1}{2}\log |\frac{\tan x}{\tan x+2}|+c$
• C. $\frac{1}{3}\log |\frac{\tan x}{\tan x+2}|+c$
• D. $-\frac{1}{3}\log |\frac{\tan x}{\tan x+2}|+c$

Answer 1

The correct option is A $\frac{1}{2}\log |\frac{\tan x}{\tan x+2}|+c$

$\int \frac{cose{c}^{2}x}{1+2cotx}dx=-\int \frac{dcotx}{1+2cotx}$
$=-\frac{1}{2}\log \mid 1+2cotx\mid +c$
$=-\frac{1}{2}\log \mid 1+\frac{2}{tanx}\mid +c$
$=-\frac{1}{2}\log \mid \frac{tanx+2}{tanx}\mid +c$
$=\frac{1}{2}\log \mid \frac{tanx}{tanx+2}\mid +c$