Evaluate ∫ 1/(9 - x^2) dx.

Question 51

MediumOriginal question

Evaluate $\int \frac{1}{9 - x^{2}}\,dx$ .

\frac{1}{3}\log\left|\frac{3 + x}{3 - x}\right| + C

Correct answerYour answer

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

Correct answerYour answer

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

Correct answerYour answer

\frac{1}{3}\tan^{-1}\frac{x}{3} + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$\int \frac{dx}{a^{2} - x^{2}} = \frac{1}{2a}\log\left|\frac{a + x}{a - x}\right| + C$ .
With $a = 3$ : $\frac{1}{6}\log\left|\frac{3 + x}{3 - x}\right| + C$ .

Worth noting

$\frac{1}{3}$ uses $\frac{1}{a}$ where the formula has $\frac{1}{2a}$ .

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