Question Number 138024 by Algoritm last updated on 09/Apr/21 Answered by TheSupreme last updated on 09/Apr/21 $${e}^{{x}} ={u} \\ $$$${dx}=\frac{\mathrm{1}}{{u}}{du} \\ $$$$\int\sqrt{{u}^{\mathrm{2}} +\mathrm{4}{u}−\mathrm{1}}\frac{{du}}{{u}} \\ $$$$\left({u}+\mathrm{2}\right)={z}…
Question Number 6947 by Tawakalitu. last updated on 03/Aug/16 $${Prove}\:{that}\: \\ $$$$ \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left\{\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{x}\:−\:{y}}{\left({x}\:+\:{y}\right)^{\mathrm{3}} }\:\:{dy}\right\}\:{dx}\:\:\:=\:\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by Yozzii last…
Question Number 138026 by mnjuly1970 last updated on 09/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:………{nice}\:\:…\:…\:…\:{calculus}……….. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Theta=\:\underset{\overset{{n}=\mathrm{1}} {\:}} {\overset{\infty} {\sum}}\left(\frac{{n}^{\mathrm{2}} }{{n}!.\mathrm{4}^{{n}} }\right)\:=?? \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 6945 by Tawakalitu. last updated on 03/Aug/16 $$\int\:\frac{{x}^{\frac{\mathrm{2}}{\mathrm{3}}} }{{x}\:+\:\mathrm{1}}\:\:{dx} \\ $$ Commented by Yozzii last updated on 03/Aug/16 $${x}={u}^{\mathrm{3}} \Rightarrow{dx}=\mathrm{3}{u}^{\mathrm{2}} {du} \\ $$$${x}^{\mathrm{2}/\mathrm{3}}…
Question Number 6938 by Tawakalitu. last updated on 03/Aug/16 $${Integrate}:\:\:\:\:\:\:\:\:\frac{{x}\:{tan}^{−\mathrm{1}} \left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx} \\ $$ Commented by Yozzii last updated on 03/Aug/16 $${I}=\int\frac{{xtan}^{−\mathrm{1}} {x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 72466 by Learner-123 last updated on 29/Oct/19 $${Prove}\:{that}\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \int_{−\sqrt{\mathrm{1}−\left({y}−\mathrm{1}\right)^{\mathrm{2}} }} ^{\:\:\mathrm{0}\:} \:{xy}^{\mathrm{2}} {dxdy}\:=\:−\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\boldsymbol{{after}}\:\mathrm{changing}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{to}\:\boldsymbol{\mathrm{polar}}\:\boldsymbol{\mathrm{form}}. \\ $$ Commented by Abdo msup. last…
Question Number 137991 by EnterUsername last updated on 08/Apr/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}^{\mathrm{3}} \left({sinx}\right){dx} \\ $$ Answered by Ar Brandon last updated on 08/Apr/21 $$\mathrm{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 72445 by aliesam last updated on 28/Oct/19 $$\int\frac{{x}\:{cos}\left({ax}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137973 by mnjuly1970 last updated on 08/Apr/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:…….{Advanced}\:…\:…\:…\:…\:{Calculus}……. \\ $$$$\:\:\:\:{prove}\:{that}::: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{8}}{ln}\left(\mathrm{2}\right)−{G}\:…\checkmark \\ $$$$\:\:\:\:{where}\:\:{G}\:{is}\:{catalan}\:{number}… \\ $$$$\:\:\: \\ $$…
Question Number 137969 by rs4089 last updated on 08/Apr/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{dx}\:{dy} \\ $$ Answered by EnterUsername last updated on 08/Apr/21…