Evaluate ∫ dx/(xlog x).

Indefinite Integrals · Question 32 of 90

Question 32

HardOriginal question

Evaluate $\int \frac{dx}{x\log x}$ .

\log\left|\log x\right| + C

Correct answerYour answer

\frac{(\log x)^{2}}{2} + C

Correct answerYour answer

\frac{1}{\log x} + C

Correct answerYour answer

\log x \cdot \log\left|x\right| + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Put $t = \log x$ , so $dt = \frac{dx}{x}$ and the integral becomes $\int \frac{dt}{t}$ .
$= \log|t| + C = \log|\log x| + C$ .

Worth noting

$\frac{(\log x)^{2}}{2}$ is $\int \frac{\log x}{x}\,dx$ : here $\log x$ is in the denominator.

Ten questions from Indefinite Integrals, at your own pace.

Ten questions from Indefinite Integrals, at your own pace.