Integrate the following functions w.r.t. x: ( x)^n x - Vidyadip

Question

Integrate the following functions w.r.t. x:

$\frac{(\log x)^n}{x}$

✓

Answer

Let $I=\int \frac{(\log x)^n}{x} d x$

Put $\log x=t . \quad \therefore \frac{1}{x} d x=d t$

$\therefore I=\int t^n d t=\frac{t^{n+1}}{n+1}+c$

$=\frac{1}{n+1} \cdot(\log x)^{n+1}+c$

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