MCQ
$\int_{\,1}^{\,x} {\frac{{\log {x^2}}}{x}\,dx = } $
- ✓${(\log x)^2}$
- B$\frac{1}{2}{(\log x)^2}$
- C$\frac{{\log {x^2}}}{2}$
- Dએકપણ નહીં.
Let $\log x = t$
==> $\frac{{dx}}{x} = dt$
$\therefore I = 2\int_0^{\log x} {t\,dt = 2\,\left[ {\frac{{{t^2}}}{2}} \right]} _0^{\log x} = {(\log x)^2}$.
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