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Find the integral of $\int \frac{dx}{9-x^{2}}$
Option: 1
$\frac{1}{6}log\left | \frac{3+x}{3-x} \right |+C$

Option: 2
$-\frac{1}{6}log\left | \frac{3+x}{3-x} \right |+C$

Option: 3
$\frac{1}{6}log\left | \frac{3-x}{3+x} \right |+C$

Option: 4
$-\frac{1}{6}log\left | \frac{3-x}{3+x} \right |+C$

Answers (1)

best_answer

Given integral,
$\int \frac{dx}{9-x^{2}}$
$\int \frac{dx}{9-x^{2}}=\int \frac{dx}{3^{2}-x^{2}}$
$\int \frac{dx}{9-x^{2}}=\frac{1}{2\left ( 3 \right )}log\left | \frac{3+x}{3-x} \right |+C$
$\int \frac{dx}{9-x^{2}}=\frac{1}{6}log\left | \frac{3+x}{3-x} \right |+C$

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Divya Prakash Singh

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