$∫\frac{dx}{x^2-9}=$

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

$∫\frac{dx}{x^2-9}=$

Options:

$\frac{1}{6}log|\frac{x-3}{x+3}|+C,$ where C is constant of integration

$\frac{1}{2}log|\frac{x-3}{x+3}|+C,$ where C is constant of integration

$\frac{1}{6}log|\frac{x+9}{x-9}|+C,$ where C is constant of integration

$\frac{1}{6}log|\frac{x+3}{x-3}|+C,$ where C is constant of integration

Correct Answer:

$\frac{1}{6}log|\frac{x-3}{x+3}|+C,$ where C is constant of integration

Explanation:

The correct answer is Option (1) → $\frac{1}{6}log|\frac{x-3}{x+3}|+C,$ where C is constant of integration

$∫\frac{dx}{x^2-9}=\frac{1}{2×3}\log\left|\frac{x-3}{x+3}\right|+C$

$\frac{1}{6}\log|\frac{x-3}{x+3}|+C$