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CUET · MATHS · PYQ PAPER 2023

The integral \(I=\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x\) is :

  1. A \(e^x \tan x+C\), where C is a constant
  2. B \(e^x \sec x+C\), where C is a constant
  3. C \(e^x \tan \left(\frac{x}{2}\right)+C\), where C is a constant
  4. D \(e^{-x} \tan \left(\frac{x}{2}\right)+C\), where C is a constant
Verified Solution

Answer & Solution

Correct Answer

(C) \(e^x \tan \left(\frac{x}{2}\right)+C\), where C is a constant

Step-by-step Solution

Detailed explanation

\(I=\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x\) \(I=\int e^x\left(\frac{1}{1+\cos x} + \frac{\sin x}{1+\cos x}\right) d x\)…