Category: Integration

Question Number 77960 by jagoll last updated on 12/Jan/20 $$\int\:\frac{\mathrm{2}{x}^{\mathrm{3}} −\mathrm{1}}{{x}^{\mathrm{4}} +{x}}\:{dx}? \\ $$ Commented by john santu last updated on 12/Jan/20 $${we}\:{divide}\:{by}\:{x}^{\mathrm{2}} \\ $$$$\int\:\frac{\mathrm{2}{x}−\frac{\mathrm{1}}{{x}^{\mathrm{2}}…

Question Number 143487 by mathmax by abdo last updated on 15/Jun/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{log}\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{t}}\mathrm{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 143474 by Ghaniy last updated on 14/Jun/21 $${for}\:{all}\:{positive}\:{integral}., \\ $$$$\:\mathrm{u}_{\mathrm{n}+\mathrm{1}} =\mathrm{u}_{\mathrm{n}} \left(\mathrm{u}_{\mathrm{n}−\mathrm{1}} ^{\mathrm{2}} −\mathrm{2}\right)−\mathrm{u}_{\mathrm{n}} \\ $$$$\:\mathrm{u}_{\mathrm{n}} =\mathrm{2}\:{and}\:\mathrm{u}_{\mathrm{1}} =\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${prove}\:{that}\::\:\mathrm{3log}_{\mathrm{2}} \left[\mathrm{u}_{\mathrm{n}} \right]=\mathrm{2}^{\mathrm{n}} −\mathrm{1}\left(−\mathrm{1}\right)^{\mathrm{n}}…

Question Number 12377 by tawa last updated on 20/Apr/17 $$\int\:\:\frac{\sqrt{\mathrm{1}\:+\:\sqrt{\mathrm{x}}}}{\mathrm{x}}\:\:\mathrm{dx} \\ $$ Answered by mrW1 last updated on 21/Apr/17 $${t}^{\mathrm{2}} =\sqrt{{x}} \\ $$$${t}^{\mathrm{4}} ={x} \\…

Question Number 77886 by mathmax by abdo last updated on 11/Jan/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \:+{x}^{−\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \:+{x}^{−\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx}…