TS EAMCET · Maths · Indefinite Integration
\(\int(\log x)^3 d x=\)
- A \((\log x)^3-3(\log x)^2+6 \log x-6+c\)
- B \(x\left[(\log x)^3-3(\log x)^2+6 \log x-6\right]+c\)
- C \((x \log x)^3-3(x \log x)^2+6 x(\log x)-6+c\)
- D \(\frac{1}{x}\left[(\log x)^3-3(\log x)^2+6 \log x-6\right]+c\)
Answer & Solution
Correct Answer
(B) \(x\left[(\log x)^3-3(\log x)^2+6 \log x-6\right]+c\)
Step-by-step Solution
Detailed explanation
\(\quad I=\int(\log x)^3 d x\) Let \(\log x=t \Rightarrow d x=e^t d t\) \(I=\int e^t t^3 d t\) Using \(\int e^x f(x) d x=e^x\left[f(x)-f^{\prime}(x)+f^{\prime \prime}(x)-\ldots.\right]\) when \(f(x)\) is polynomial function…
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