WBJEE · Maths · Indefinite Integration
\(\int \frac{\log \sqrt{\mathrm{x}}}{3 \mathrm{x}} \mathrm{dx}\) is equal to
- A \(\frac{1}{3}(\log \sqrt{\mathrm{x}})^2+\mathrm{C}\)
- B \(\frac{2}{3}(\log \sqrt{\mathrm{x}})^2+\mathrm{C}\)
- C \(\frac{2}{3}(\log x)^2+C\)
- D \(\frac{1}{3}(\log x)^2+C\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3}(\log \sqrt{\mathrm{x}})^2+\mathrm{C}\)
Step-by-step Solution
Detailed explanation
Hints : \(\mathrm{x}=\mathrm{t}^2 \Rightarrow \int \frac{\ell \mathrm{nt}}{3 \mathrm{t}^2}(2 \mathrm{tdt})=\frac{2}{3} \int \frac{\ell \mathrm{nt}}{\mathrm{t}} \mathrm{dt}=\frac{2}{3} \frac{(\ell \mathrm{nt})^2}{2}+\mathrm{c}=\frac{(\ln \sqrt{\mathrm{x}})^2}{3}+\mathrm{c}\)
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