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CBSE Class 12 · 2008 · Indefinite IntegralsVery Short Answer

Evaluate :

\int \frac{x ^{2}}{1 + x ^{3}} d x

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

Solution

Put

t = 1 + x^{3}

, so

d t = 3 x^{2} d x

, i.e.

x^{2} d x = \frac{d t}{3}

. Then

\frac{1}{3} \int \frac{d t}{t} = \frac{1}{3} lo g ∣ t ∣ + C .

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

CBSE Class 12 Board · 2008 · Subjective

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