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CBSE Class 12 · 2020 · Indefinite IntegralsVery Short Answer

Find

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

Answer: $\frac{3}{2} (x^{2} + 1)^{2/3} + C$

Solution

Put

t = x^{2} + 1

, so

d t = 2 x d x

. Then

\int t^{- 1/3} d t = \frac{t ^{2/3}}{2/3} + C = \frac{3}{2} t^{2/3} + C .

\frac{3}{2} (x^{2} + 1)^{2/3} + C

CBSE Class 12 Board · 2020 · Subjective

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