Question Number 130684 by mathmax by abdo last updated on 28/Jan/21
![1)calculate ∫ (dx/((x−1)(x−2)....(x−n))) ( n integr natural) 2) find the value of U_n =∫_(n+1) ^∞ (dx/((x−1)(x−2)....(x−n)))](https://www.tinkutara.com/question/Q130684.png)
$$\left.\mathrm{1}\right)\mathrm{calculate}\:\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)….\left(\mathrm{x}−\mathrm{n}\right)}\:\:\:\left(\:\mathrm{n}\:\mathrm{integr}\:\mathrm{natural}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{n}+\mathrm{1}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)….\left(\mathrm{x}−\mathrm{n}\right)} \\ $$