Evaluate ∫ dx/(x^2 - 5x + 6).

Question 66

MediumOriginal question

Evaluate $\int \frac{dx}{x^{2} - 5x + 6}$ .

\log\left|\frac{x - 2}{x - 3}\right| + C

Correct answerYour answer

\log\left|(x - 2)(x - 3)\right| + C

Correct answerYour answer

\log\left|\frac{x - 3}{x - 2}\right| + C

Correct answerYour answer

\frac{1}{2}\log\left|\frac{x - 3}{x - 2}\right| + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$\frac{1}{(x - 2)(x - 3)} = \frac{A}{x - 2} + \frac{B}{x - 3}$ : $x = 2$ gives $A = -1$ , $x = 3$ gives $B = 1$ .
$\int \left(\frac{1}{x - 3} - \frac{1}{x - 2}\right)dx = \log\left|\frac{x - 3}{x - 2}\right| + C$ .

Worth noting

The fraction turned upside down comes from swapping the signs of $A$ and $B$ .

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