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} \\ $$$${tanx}={t}\:\Rightarrow{w}=\int\:\:\frac{{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\left(\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 160590 by mnjuly1970 last updated on 02/Dec/21 $$ \\ $$$$\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \frac{\:{arcsinh}\left({x}\right)}{{x}}\:{dx}\:\overset{?} {=}\:\frac{\pi^{\mathrm{2}} }{\mathrm{20}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 29517 by yesaditya22@gmail.com last updated on 09/Feb/18 $$\int\mathrm{x}^{\mathrm{6}} −\mathrm{1}/\mathrm{x}^{\mathrm{2}} +\mathrm{1} \\ $$ Commented by abdo imad last updated on 09/Feb/18 $${let}\:{put}\:{I}=\:\int\:\frac{{x}^{\mathrm{6}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}\:=\:\int\:\frac{{x}^{\mathrm{6}}…
Question Number 29506 by abdo imad last updated on 09/Feb/18 $${le}\:{give}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{sin}\left(\left(\mathrm{2}{n}−\mathrm{1}\right){x}\right)}{{sinx}}{dx}\:{and}\:{B}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{sin}^{\mathrm{2}} \left({nx}\right)}{{sin}^{\mathrm{2}} {x}}{dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{B}_{{n}+\mathrm{1}} −{B}_{{n}} =\:{A}_{{n}+\mathrm{1}}…
Question Number 160563 by qaz last updated on 02/Dec/21 $$\int\mathrm{x}\left\{\mathrm{x}\right\}\left[\mathrm{x}\right]\mathrm{dx}=? \\ $$ Answered by mr W last updated on 02/Dec/21 $$\left[{x}\right]={n} \\ $$$$\left\{{x}\right\}={x}−{n} \\ $$$$\int{x}\left\{{x}\right\}\left[{x}\right]{dx}…
Question Number 160556 by amin96 last updated on 01/Dec/21 $$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{arctg}}\left(\boldsymbol{\mathrm{x}}\right)}{\mathrm{1}+\boldsymbol{\mathrm{x}}}\centerdot\frac{\boldsymbol{\mathrm{dx}}}{\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{x}}}}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com