Question:
Write a value of $\int \frac{(\log x)^{n}}{x} d x$.
Solution:
let $\log x=t$
Differentiating on both sides we get,
$\frac{1}{x} d x=d t$
Substituting above equations in $\int \frac{(\log x)^{n}}{x} d x$ we get,
$\int t^{n} d t$
$=\frac{t^{n+1}}{n+1}+c$
$=\frac{(\log x)^{n+1}}{n+1}+c$
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