$\int \frac{d x}{\cos ^2(x)+\sin (2 x)}=$

Question

Aicharya · Accepted Answer

$I=\int \frac{d x}{\cos ^2 x+\sin 2 x}=\int \frac{\sec ^2 x d x}{1+2 \tan x}$ Put $1+2 \tan x=t \Rightarrow \sec ^2 x d x=\frac{d t}{2}$ So, $I=\frac{1}{2} \int \frac{d t}{t}=\frac{1}{2} \log _e|t|+C=\frac{1}{2} \log _e|1+2 \tan x|+C$ Hence, option (c) is correct.

\(\int \frac{d x}{\cos ^2(x)+\sin (2 x)}=\)

Solution