TS EAMCET · Maths · Indefinite Integration
If \(\int x^3(\log x)^2 d x=x^4\left[A(\log x)^2+B(\log x)\right.\) \(+C \log e]+K\), then \(A+B+C\)
- A \(\frac{7}{24}\)
- B \(\frac{4}{25}\)
- C \(\frac{3}{14}\)
- D \(\frac{5}{32}\)
Answer & Solution
Correct Answer
(D) \(\frac{5}{32}\)
Step-by-step Solution
Detailed explanation
We have, \(\int x^3(\log x)^2 d x=x^4\) \(\left[A(\log x)^2+B(\log x)+C \log e\right]+K\) Now, \(\int x^3(\log x)^2 d x\) \(=(\log x)^2 \int x^3 d x-\int\left(\frac{d}{d x}(\log x)^2 \int x^3 d x\right) d x\)…
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