AP EAMCET · Maths · Indefinite Integration
\(\int(\log 2 \mathrm{x})^3 \mathrm{dx}=\)
- A \(x\left[(\log 2 x)^3-3(\log 2 x)^2+6(\log 2 x)-6\right]+c\)
- B \(\frac{x}{4}\left[4(\log 2 x)^3-6(\log 2 x)^2+6(\log 2 x)-3\right]+c\)
- C \(\frac{x}{2}\left[(\log 2 x)^3-3(\log 2 x)^2+3(\log 2 x)-6\right]+c\)
- D \(x\left[(\log 2 x)^3-6(\log 2 x)^2+18(\log 2 x)-54\right]+c\)
Answer & Solution
Correct Answer
(A) \(x\left[(\log 2 x)^3-3(\log 2 x)^2+6(\log 2 x)-6\right]+c\)
Step-by-step Solution
Detailed explanation
\(\int(\log 2 x)^3 dx = x(\log 2 x)^3 - 3 \int(\log 2 x)^2 dx\) \(\int(\log 2 x)^2 dx = x(\log 2 x)^2 - 2 \int(\log 2 x) dx\) \(\int(\log 2 x) dx = x(\log 2 x) - \int 1 dx = x(\log 2 x) - x\)…
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