AP EAMCET · Maths · Indefinite Integration
\(\int(\log x)^2 x^3 d x=\frac{x^4}{32} f(x)+C \Rightarrow f(x)=\)
- A \(8(\log x)^2-4 \log x+1\)
- B \(8 \log x-4 x^4+x^3\)
- C \(8(\log x)^2+4 x-x^2\)
- D \(4(\log x)^2-4 x^2+x+1\)
Answer & Solution
Correct Answer
(A) \(8(\log x)^2-4 \log x+1\)
Step-by-step Solution
Detailed explanation
\(I=\int(\log x)^2 x^3 d x\) Using integration by parts, \(I=(\log x)^2 \int x^3 d x-\int\left(\frac{d(\log x)^2}{d x} \int x^3 d x\right) d x\)…
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