AP EAMCET · Maths · Indefinite Integration
\(\int\left[(\log 2 x)^2+2 \log 2 x\right] d x=\)
- A \((\log 2 x)^2+c\)
- B \(2 x \log 2 x+c\)
- C \(x(\log 2 x)^2+c\)
- D \(2 x(\log x)^2+c\)
Answer & Solution
Correct Answer
(C) \(x(\log 2 x)^2+c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{I}=\int\left[(\log 2 x)^2+2 \log 2 x\right] d x=\int(\log 2 x)^2 d x+2 \int \log 2 x d x \\ I= & x(\log 2 x)^2-2 \int \log 2 x d x+2 \int \log 2 x d x+c \\ I= & x(\log 2 x)^2+c\end{aligned}\)
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