Question Number 10555 by paonky last updated on 17/Feb/17
![why Γ(x)=∫_0 ^1 [−ln(u)]^(x−1) du ? I don′t know how to prove this](https://www.tinkutara.com/question/Q10555.png)
$$\mathrm{why}\:\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \left[−\mathrm{ln}\left(\mathrm{u}\right)\right]^{{x}−\mathrm{1}} {du}\:\:? \\ $$$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{this} \\ $$