Evaluate ∫ x^2/(x^2 - 4) dx.

Question 71

HardOriginal question

Evaluate $\int \frac{x^{2}}{x^{2} - 4}\,dx$ .

x + \log\left|\frac{x - 2}{x + 2}\right| + C

Correct answerYour answer

\log\left|\frac{x - 2}{x + 2}\right| + C

Correct answerYour answer

x + \log\left|\frac{x + 2}{x - 2}\right| + C

Correct answerYour answer

x + 4\log\left|\frac{x - 2}{x + 2}\right| + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The fraction is improper: $\frac{x^{2}}{x^{2} - 4} = 1 + \frac{4}{x^{2} - 4}$ .
$\int \frac{4\,dx}{x^{2} - 4} = 4 \cdot \frac{1}{4}\log\left|\frac{x - 2}{x + 2}\right|$ , so the integral is $x + \log\left|\frac{x - 2}{x + 2}\right| + C$ .

Worth noting

Leaving out $x$ forgets the 1 that the division gives first.

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