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CBSE Class 12 · 2009 · Indefinite IntegralsVery Short Answer

Evaluate :

\int \frac{( 1 + l o g x ) ^{2}}{x} d x

Answer: $\frac{( 1 + lo g x ) ^{3}}{3} + C$

Solution

Put

t = 1 + lo g x

, so

d t = \frac{1}{x} d x

. Then

\int t^{2} d t = \frac{t ^{3}}{3} + C .

\frac{( 1 + lo g x ) ^{3}}{3} + C

CBSE Class 12 Board · 2009 · Subjective

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