Question:
Evaluate the following integrals:
$\int \frac{1}{x}(\log x)^{2} d x$
Solution:
Assume $\log x=t$
$d(\log (x))=d t$
$\Rightarrow \frac{1}{x} d x=d t$
$\therefore$ Substituting $\mathrm{t}$ and $\mathrm{dt}$ in given equation we get
$\Rightarrow \int \mathrm{t}^{2} \cdot \mathrm{dt}$
$\Rightarrow \int \mathrm{t}^{2} \cdot \mathrm{dt}$
$\Rightarrow \frac{t^{3}}{3}+c$
But $\log x=t$
$\Rightarrow \frac{(\log (x))^{3}}{3}+C$
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