Integrals
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
The value of $\int \frac{x^2}{1+x^3} dx$ is:
(a) $\frac{1}{3} \log|1+x^3| + C$
(b) $\log|1+x^3| + C$
(c) $\frac{1}{3 (1+x^3)^2} + C$
(d) $3 \log|1+x^3| + C$
Step-by-Step Solution
Substitute t = 1+x^3, dt = 3x^2 dx. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $\frac{1}{3} \log|1+x^3| + C$: 1.0 Mark
Correct Answer: $\frac{1}{3} \log|1+x^3| + C$
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