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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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