ExamBro
Web Login Download App
ExamBro
Download App
CUET · MATHS · PYQ PAPER 2025

For \(x \in\left(0, \frac{\pi}{2}\right), \int \frac{1}{\sin ^2 x+\sin 2 x} d x\) is equal to

  1. A \(\frac{1}{2} \log \left|\frac{\tan x+2}{\tan x-2}\right|+C\), where \(C\) is constant of integration
  2. B \(\frac{1}{2} \log \left|\frac{\tan x}{\tan x+2}\right|+C\), where \(C\) is constant of integration
  3. C \(\frac{1}{2} \log \left|\frac{\tan x+2}{\tan x}\right|+C\), where \(C\) is constant of integration
  4. D \(\frac{1}{2} \log \left|\frac{\tan x+1}{\tan x+2}\right|+C\), where \(C\) is constant of integration
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{1}{2} \log \left|\frac{\tan x}{\tan x+2}\right|+C\), where \(C\) is constant of integration

Step-by-step Solution

Detailed explanation

\(I = \int \frac{1}{\sin ^2 x+2 \sin x \cos x} d x\) \(I = \int \frac{\frac{1}{\cos ^2 x}}{\frac{\sin ^2 x}{\cos ^2 x}+\frac{2 \sin x \cos x}{\cos ^2 x}} d x\) \(I = \int \frac{\sec ^2 x}{\tan ^2 x+2 \tan x} d x\) Let \(u=\tan x \implies du=\sec ^2 x d x\)…
Same subject

More questions from MATHS

Explore more questions on app
From CUET

More PYQs from CUET

Explore more questions on app