Evaluate the following integrals:

Question:

Evaluate the following integrals:

$\int \frac{\log x^{2}}{x} d x$

Solution:

Assume $\log x=t$

$\Rightarrow \mathrm{d}(\log \mathrm{x})=\mathrm{dt}$

$\Rightarrow \frac{1}{\mathrm{x}} \mathrm{dx}=\mathrm{dt}$

Substituting the values oft and dt we get

$\Rightarrow \int \mathrm{t}^{2} \mathrm{dt}$

$\Rightarrow \frac{\mathrm{t}^{3}}{3}+\mathrm{c}$

But $t=\log x$

$\Rightarrow \frac{\log ^{3} x}{3}+c$

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