Evaluate the following integrals:


Evaluate $\int \frac{\log x}{x^{3}} d x$


Use method of integration by parts

$y=\log x \int \frac{1}{x^{3}} d x-\int \frac{d}{d x} \log x\left(\int \frac{1}{x^{3}} d x\right) d x$

$y=-\log x \frac{1}{2 x^{2}}+\int \frac{1}{2 x^{3}} d x$

$y=-\frac{1}{2 x^{2}} \log x-\frac{1}{4 x^{2}}+c$

$y=-\frac{1}{4 x^{2}}(2 \log x+1)+c$

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