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Category: Integration

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-

Question Number 130684 by mathmax by abdo last updated on 28/Jan/21 $$\left.\mathrm{1}\right)\mathrm{calculate}\:\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)….\left(\mathrm{x}−\mathrm{n}\right)}\:\:\:\left(\:\mathrm{n}\:\mathrm{integr}\:\mathrm{natural}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{n}+\mathrm{1}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)….\left(\mathrm{x}−\mathrm{n}\right)} \\ $$ Terms of Service Privacy Policy Contact:…

3-x-x-1-dx-

Question Number 130678 by EDWIN88 last updated on 28/Jan/21 $$\:\int\:\frac{\mathrm{3}\sqrt{{x}}}{{x}−\mathrm{1}}\:{dx}\:?\: \\ $$ Answered by liberty last updated on 28/Jan/21 $$\mathrm{L}\:=\:\int\:\frac{\mathrm{3}\sqrt{\mathrm{x}}}{\mathrm{x}−\mathrm{1}}\:\mathrm{dx}\:;\:\left[\:\mathrm{x}=\mathrm{u}^{\mathrm{2}} \:\right] \\ $$$$\mathrm{L}=\mathrm{6}\int\:\frac{\mathrm{u}^{\mathrm{2}} }{\mathrm{u}^{\mathrm{2}} −\mathrm{1}}\:\mathrm{du}\:=\:\mathrm{6}\int\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{u}^{\mathrm{2}}…

dx-x-2-3-x-1-2-

Question Number 65137 by Tony Lin last updated on 25/Jul/19 $$\int\frac{{dx}}{\left({x}−\mathrm{2}\right)^{\mathrm{3}} \left({x}+\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$ Commented by mathmax by abdo last updated on 25/Jul/19 $${let}\:{I}\:=\int\:\:\:\frac{{dx}}{\left({x}−\mathrm{2}\right)^{\mathrm{3}}…