- #1

v0id19

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## Homework Statement

If

*n*is a positive integer, prove that [tex]\int_{0}^{1}(\ln{x})^ndx=(-1)^n\cdot n![/tex]

## Homework Equations

## The Attempt at a Solution

I'm assuming that since ln(0) is undef and [tex]\mathop{\lim}\limits_{x \to 0^+}\ln{x}=- \infty[/tex] i need to rewrite the integral as [tex]\mathop{\lim}\limits_{t \to 0^+}\int_{t}^{1}(\ln{x})^ndx=(-1)^n\cdot n![/tex]. But I have no idea how to integrate that since

*n*is a variable...