Question Number 115761 by mnjuly1970 last updated on 28/Sep/20 $$\:\:\:\:\:\:….\:\:\:{advanced}\:\:{calculus}…\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:…\:\:\:{evaluate}\:…\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Psi=\:\int_{−\infty} ^{\:+\infty} \left(\frac{{x}}{\mathrm{2}+\mathrm{2}^{−{x}} +\mathrm{2}^{{x}} }\right)^{\mathrm{2}} {dx}\:=??? \\ $$$$\:{m}.{n}.{july}\:\mathrm{70}…
Question Number 50219 by cesar.marval.larez@gmail.com last updated on 14/Dec/18 Answered by peter frank last updated on 15/Dec/18 $${all}\:{question}\:{above}\:\:{lie}\:{on}\:{the}\:{concept}\left({partial}\:{fraction}\right) \\ $$$$\int\frac{\mathrm{5x}+\mathrm{3}}{\mathrm{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2x}}=\int\frac{\mathrm{5x}+\mathrm{3}}{{x}\left({x}+\mathrm{1}\right)\left({x}−\mathrm{3}\right)} \\ $$$$\frac{\mathrm{A}}{\mathrm{x}\:}+\frac{\mathrm{B}}{\mathrm{x}−\mathrm{3}\:}+\frac{\mathrm{C}}{\mathrm{x}+\mathrm{1}} \\…
Question Number 115743 by bemath last updated on 28/Sep/20 $$\int\:{e}^{{ax}} .\mathrm{sin}\:{bx}\:{dx}\:=? \\ $$$${by}\:{complex}\:{number} \\ $$ Answered by Ar Brandon last updated on 28/Sep/20 $$\mathcal{I}=\int\mathrm{e}^{\mathrm{a}{x}} \mathrm{sinb}{x}\mathrm{d}{x}=\frac{\mathrm{1}}{\mathrm{2}{i}}\int\mathrm{e}^{\mathrm{a}{x}}…
Question Number 115725 by Bird last updated on 28/Sep/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{\left({x}^{\mathrm{2}\:} +{x}+\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by mathmax by abdo last updated on 28/Sep/20…
Question Number 50186 by rahul 19 last updated on 14/Dec/18 $${Let}\:{f}\left({x}\right)=\:\int_{\mathrm{2}} ^{\:{x}} \:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{6}} }. \\ $$$${Prove}\:{that}\:\::\:\frac{\mathrm{1}}{\mathrm{730}}<{f}\left(\mathrm{3}\right)<\frac{\mathrm{1}}{\mathrm{65}}. \\ $$ Answered by mr W last updated on…
Question Number 50161 by cesar.marval.larez@gmail.com last updated on 14/Dec/18 $${Find}\:{the}\:{function}\:{whose}\:{first}\: \\ $$$${derivative}\:{is}\:\mathrm{8}−\frac{\mathrm{5}}{\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} }}\:{the}\:{initial}\: \\ $$$${conditions}\:{f}\left(\mathrm{8}\right)=−\mathrm{20} \\ $$ Answered by afachri last updated on 14/Dec/18 $${F}\left({x}\right)\:\:=\:\:\int\:{f}'\left({x}\right)\:\:{dx}…
Question Number 50158 by cesar.marval.larez@gmail.com last updated on 14/Dec/18 Commented by cesar.marval.larez@gmail.com last updated on 14/Dec/18 $${i}\:{am}\:{practicing}\:{very}\:{hard} \\ $$ Answered by afachri last updated on…
Question Number 115689 by Algoritm last updated on 27/Sep/20 Answered by mathmax by abdo last updated on 27/Sep/20 $$\mathrm{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\right)}{\mathrm{x}}\mathrm{dx}\:\:\mathrm{changement}\:\mathrm{x}\:=\mathrm{sint}\:\mathrm{give} \\ $$$$\mathrm{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 115664 by bemath last updated on 27/Sep/20 $${If}\:\underset{{x}\rightarrow{p}} {\mathrm{lim}}\:\frac{{p}^{{x}} −{x}^{{p}} }{{x}^{{x}} −{p}^{{p}} }\:=\:\mathrm{1}\:{then}\:{p}\:=\:? \\ $$ Answered by Olaf last updated on 27/Sep/20 $${x}\:=\:{p}+{u}…
Question Number 115656 by bobhans last updated on 27/Sep/20 $$\int\:\sqrt{\frac{{x}−{a}}{{b}−{x}}}\:{dx}\:=\:? \\ $$$${where}\:{a}\:<{x}\:<\:{b} \\ $$ Commented by bemath last updated on 27/Sep/20 $${I}=\:\int\:\sqrt{\frac{{x}−{a}}{−{x}+{b}}}\:{dx}\: \\ $$$${I}\:=\:−\sqrt{\left({x}−{a}\right)\left({b}−{x}\right)}\:−\left({a}+{b}\right)\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{\frac{{b}−{x}}{{a}+{b}}}\right)+{C}…