$\int \frac{d x}{1+\tan x}$ is equal to:

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$\int \frac{d x}{1+\tan x}$ is equal to:

Options:

$\frac{x}{2}+\frac{1}{2} \log |\cos x-\sin x|+c$, C is an arbitrary constant

$\frac{x}{2}+\frac{1}{2} \log |\cos x+\sin x|+c$, C is an arbitrary constant

$\frac{x}{2}-\frac{1}{2} \log |\cos x-\sin x|+c$, C is an arbitrary constant

$\frac{x}{2}-\frac{1}{2} \log |\cos x+\sin x|+c$, C is an arbitrary constant

Correct Answer:

$\frac{x}{2}+\frac{1}{2} \log |\cos x+\sin x|+c$, C is an arbitrary constant

Explanation:

The correct answer is Option (2) → $\frac{x}{2}+\frac{1}{2} \log |\cos x+\sin x|+c$, C is an arbitrary constant