CUET · MATHS · PYQ PAPER 2023
The value of the integral \(\int \frac{\log x^3}{x} d x\) is :
- A \(\frac{2}{3}(\log x)^2+C\), where \(C\) is a constant
- B \(\frac{3}{2}(\log x)^2+C\), where C is a constant
- C \(\log x^2+C\), where C is a constant
- D \(\log x^3+C\), where C is a constant
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}(\log x)^2+C\), where C is a constant
Step-by-step Solution
Detailed explanation
\(\int \frac{\log x^3}{x} d x = \int \frac{3 \log x}{x} d x\) Let \(u = \log x\). Then \(du = \frac{1}{x} dx\). \(\int 3u \, du = 3 \frac{u^2}{2} + C = \frac{3}{2}(\log x)^2+C\)
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