COMEDK · Maths · 28. Indefinite Integration
\(\int \log x(\log x+2) d x \text { equals to }\)
- A \(x\left[1+(\log x)^2\right]+C\)
- B \(2 x \log x+C\)
- C \(x(1+\log x)^2+C\)
- D \(x(\log x)^2+C\)
Answer & Solution
Correct Answer
(D) \(x(\log x)^2+C\)
Step-by-step Solution
Detailed explanation
Let \(I = \int \log x(\log x + 2) dx\). Expanding the integrand, we get \(I = \int ((\log x)^2 + 2 \log x) dx\). Consider the function \(f(x) = x(\log x)^2\). Differentiating \(f(x)\) with respect to \(x\) using the product rule:…
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