Evaluate the following integrals:

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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