Q87 / 160 · WBJEE 2010 · Mathematics

$\int \frac{\log \sqrt{\mathrm{x}}}{3 \mathrm{x}} \mathrm{dx}$ is equal to

  • Correct answer
    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
    $\frac{1}{3}(\log x)^2+C$

Solution

Hints : $\mathrm{x}=\mathrm{t}^2 \Rightarrow \int \frac{\ell \mathrm{nt}}{3 \mathrm{t}^2}(2 \mathrm{tdt})=\frac{2}{3} \int \frac{\ell \mathrm{nt}}{\mathrm{t}} \mathrm{dt}=\frac{2}{3} \frac{(\ell \mathrm{nt})^2}{2}+\mathrm{c}=\frac{(\ln \sqrt{\mathrm{x}})^2}{3}+\mathrm{c}$

Hence, the correct answer is option: 'A'.

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