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Integral Calculus

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Question : 34 of 73

Marks: +1, -0

Evaluate

\int \frac{1}{x \log x} \, dx

$\log\left(\log \frac{x^{2}}{2}\right) + c$
$\log(\log x) + c$
$\log(\log x^{2}) + c$
None

Solution:

Concept:

Substitution method: set

u = \log x

to simplify the integral.

Explanation:

Let

u = \log x

.

Then

du = \frac{1}{x} dx

.

The integral becomes

\int \frac{1}{u} du = \log|u| + c = \log|\log x| + c

.

Since

\log x > 0

for

x > 1

(common domain), we write

\log(\log x) + c

.

Answer:

\log(\log x) + c

corresponds to option B.

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