CUET · MATHS · PYQ PAPER 2025
The value of \(\int_1^3 \frac{x^2}{x^3+1} d x\)
- A \(\frac{1}{3} \log 26\)
- B \(\log 14\)
- C \(\frac{1}{3} \log 14\)
- D \(\log 56\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{3} \log 14\)
Step-by-step Solution
Detailed explanation
\(\int_1^3 \frac{x^2}{x^3+1} d x = \frac{1}{3} \int_1^3 \frac{3x^2}{x^3+1} d x\) \( = \frac{1}{3} [\log|x^3+1|]_1^3 \) \( = \frac{1}{3} (\log|3^3+1| - \log|1^3+1|) \) \( = \frac{1}{3} (\log 28 - \log 2) \) \( = \frac{1}{3} \log \left(\frac{28}{2}\right) \)…
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