Question Number 95115 by bobhans last updated on 23/May/20 $$\int\:\mathrm{e}^{\:{x}} \:\sqrt{\mathrm{1}+{e}^{\:\mathrm{2}{x}} }\:{dx}\:=\:?\: \\ $$ Answered by i jagooll last updated on 23/May/20 Commented by bobhans…
Question Number 160645 by tounghoungko last updated on 03/Dec/21 $$\:\int\:\mathrm{sin}\:^{\mathrm{8}} \mathrm{x}\:\mathrm{dx}\:=? \\ $$ Commented by swamy1234 last updated on 04/Dec/21 good Answered by puissant last…
Question Number 29574 by yesasitya22@gmail.com last updated on 10/Feb/18 $$\int{x}^{\mathrm{6}} −\mathrm{1}/{x}^{\mathrm{2}} −\mathrm{1}{dx} \\ $$ Commented by tawa tawa last updated on 10/Feb/18 $$\int\:\frac{\mathrm{x}^{\mathrm{6}} \:−\:\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{1}}\:\mathrm{dx}…
Question Number 160636 by mnjuly1970 last updated on 03/Dec/21 $$ \\ $$$$\:\:\:\:\:\:\:\:{prove}\:{that} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}\:\:} ^{\:\mathrm{1}} \left(\frac{{tanh}^{\:−\mathrm{1}} \left(\:{x}\:\right)}{{x}}\:\right)^{\:\mathrm{2}} =\:\zeta\:\left(\:\mathrm{2}\:\right)\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\:\: \\ $$$$ \\ $$$$ \\…
Question Number 29553 by abdo imad last updated on 09/Feb/18 $${let}\:{put}\:\:{I}\left({x}\right)=\:\int_{{x}} ^{+\infty} \:\frac{{sin}^{\mathrm{3}} {t}}{{t}^{\mathrm{2}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$${find}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{I}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}^{\mathrm{3}} {t}}{{t}^{\mathrm{2}} }{dt}\:.…
Question Number 29552 by abdo imad last updated on 09/Feb/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\sqrt{{x}+\mathrm{1}}\:−\mathrm{1}}{{x}\left({x}+\mathrm{1}\right)}{dx}\:. \\ $$ Commented by prof Abdo imad last updated on 11/Feb/18 $${let}\:{put}\:{I}\:=\:\int_{\mathrm{0}}…
Question Number 29551 by abdo imad last updated on 09/Feb/18 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left(\mathrm{2}{x}\right)−{arctanx}}{{x}}{dx}. \\ $$ Commented by prof Abdo imad last updated on 11/Feb/18 $${let}\:{put}\:{I}=\int_{\mathrm{0}}…
Question Number 160597 by cortano last updated on 03/Dec/21 $$\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{dx}}{\mathrm{2}−\mathrm{cos}\:\mathrm{x}}\:=? \\ $$ Answered by Mathspace last updated on 03/Dec/21 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{\mathrm{2}−{cosx}}\:{we}\:{do}\:{the}\:{changement} \\…
Question Number 95060 by EmericGent last updated on 22/May/20 $${Evaluate} \\ $$$$\int_{\mathrm{0}} ^{\infty} {arcsin}\left({e}^{-{x}} \right)\:{dx} \\ $$$$\int_{\mathrm{0}} ^{\infty} {arccos}\left(\mathrm{1}-\mathrm{2}{e}^{-{x}} \right)\:{dx} \\ $$$${and}\:{Step}\:{Up} \\ $$$${Evaluate} \\…
Question Number 160594 by cortano last updated on 03/Dec/21 $$\:\:\:\:\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:=? \\ $$ Answered by Mathspace last updated on 03/Dec/21 $${w}=\int\:\:\frac{{dx}}{\mathrm{1}−{tan}^{\mathrm{2}} {x}}\:{we}\:{do}\:{the}\:{changement} \\ $$$${tanx}={t}\:\Rightarrow{w}=\int\:\:\frac{{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\left(\mathrm{1}−{t}^{\mathrm{2}}…