Menu Close

Category: Integration

1-find-dx-x-2-x-1-3-x-2-1-2-calculate-1-3-dx-x-2-x-1-3-x-2-1-

Question Number 57230 by maxmathsup by imad last updated on 31/Mar/19 $$\left.\mathrm{1}\right)\:{find}\:\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} \:+\mathrm{1}\right)} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}} \:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} \:+\mathrm{1}\right)} \\ $$ Terms…

let-f-0-1-arctan-x-1-x-2-dx-with-real-1-find-f-interms-of-2-find-the-values-of-0-1-arctan-2x-1-2x-2-dx-and-0-1-arctan-4x-1-4x-2-dx-

Question Number 57227 by maxmathsup by imad last updated on 31/Mar/19 $${let}\:{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+\alpha{x}^{\mathrm{2}} }\:{dx}\:\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}\left(\alpha\right)\:{interms}\:{of}\:\alpha \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }\:{dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{arctan}\left(\mathrm{4}{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }{dx}…

1-calculate-f-a-0-a-2x-1-x-2-x-3-x-2-1-dx-1-calculate-f-1-and-f-2-

Question Number 57225 by maxmathsup by imad last updated on 31/Mar/19 $$\left.\mathrm{1}\right){calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{{a}} \:\:\:\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}^{\mathrm{2}} \:−{x}+\mathrm{3}\right)\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)}{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\mathrm{1}\right){and}\:{f}\left(\mathrm{2}\right) \\ $$ Commented by maxmathsup by imad…