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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