Integrals
NCERT Class 12
CBSE
Grade 12
Question:
$\int \dfrac{dx}{x(x^2 + 1)}$ is equal to:
(a) $\log|x| - \dfrac{1}{2} \log(x^2 + 1) + C$
(b) $\log|x| + \dfrac{1}{2} \log(x^2 + 1) + C$
(c) $\dfrac{1}{2} \log|x| - \log(x^2 + 1) + C$
(d) $\log(x^2 + 1) - \log|x| + C$
Step-by-Step Solution
$\dfrac{1}{2} \int \left( \dfrac{1}{t} - \dfrac{1}{t+1} \right) dt = \log|x| - \dfrac{1}{2} \log(x^2 + 1) + C$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating integral $= \log|x| - (1/2)\log(x^2+1) + C$: 1.0 Mark
Correct Answer: $\log|x| - \dfrac{1}{2} \log(x^2 + 1) + C$
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