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Category: Integration

Question-170802

Question Number 170802 by Sotoberry last updated on 31/May/22 Answered by thfchristopher last updated on 31/May/22 $$\int\mathrm{ln}\:\left({x}+{x}^{\mathrm{2}} \right){dx} \\ $$$$=\int\mathrm{ln}\:{x}\left({x}+\mathrm{1}\right){dx} \\ $$$$=\int\mathrm{ln}\:{xdx}+\int\mathrm{ln}\:\left({x}+\mathrm{1}\right){dx} \\ $$$$={x}\mathrm{ln}\:{x}−\int{xd}\left(\mathrm{ln}\:{x}\right)+{x}\mathrm{ln}\:\left({x}+\mathrm{1}\right)−\int{xd}\left[\mathrm{ln}\:\left({x}+\mathrm{1}\right)\right] \\…

p-5-6-p-p-8-11-p-11-13-12ky-x-2-6x-dx-p-4-7-p-p-9-12-p-11-16-x-2-y-3-2-k-dx-solve-for-y-

Question Number 105239 by bemath last updated on 27/Jul/20 $$\underset{\underset{{p}=\mathrm{5}} {\overset{\mathrm{6}} {\sum}}{p}} {\overset{\underset{{p}=\mathrm{8}} {\overset{\mathrm{11}} {\sum}}{p}} {\sum}}\:\underset{\mathrm{11}} {\overset{\mathrm{13}} {\int}}\left(\frac{\mathrm{12}{ky}}{{x}^{\mathrm{2}} }\:+\:\mathrm{6}{x}\right)\:{dx}\:=\:\underset{\underset{{p}=\mathrm{4}} {\overset{\mathrm{7}} {\sum}}{p}} {\overset{\underset{{p}=\mathrm{9}} {\overset{\mathrm{12}} {\sum}}{p}} {\sum}}\:\underset{\mathrm{11}}…

let-S-n-0-n-x-1-x-x-1-x-3-dx-1-calculate-S-n-2-find-lim-n-S-n-

Question Number 39660 by abdo mathsup 649 cc last updated on 09/Jul/18 $${let}\:\:{S}_{{n}} \:\:=\:\int_{\mathrm{0}} ^{{n}} \:\:\:\:\:\frac{{x}\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\left({x}+\mathrm{1}\:−\left[{x}\right]\right)^{\mathrm{3}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{S}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:{S}_{{n}} \\ $$…