$\int \frac{dx}{1+\sin x}$ is equal to

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$\int \frac{dx}{1+\sin x}$ is equal to

Options:

$\sec x+\tan x+C$

$\tan x-\sec x+C$

$\sec x-\tan x+C$

None

Correct Answer:

$\tan x-\sec x+C$

Explanation:

$I=\int \frac{1}{1+\sin x}×\frac{1-\sin x}{1-\sin x}dx=\int\frac{1+\sin x}{\cos^2x}dx=\int\sec^2x-\sec x\tan xdx$

$=\tan x-\sec x+C$