Question Number 50388 by Abdo msup. last updated on 16/Dec/18 $${find}\:{inf}_{\left({a},{b}\right)\in{R}^{\mathrm{2}} } \:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} \left({ln}\left({x}\right)−{ax}−{b}\right)^{\mathrm{2}} {dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 115920 by mnjuly1970 last updated on 29/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:{prove}\:\:\:{that}\::: \\ $$$$\: \\ $$$$\:\int_{\mathrm{0}} ^{\:\infty} \left({tanh}^{{a}} \left({x}\right)\:−{tanh}^{{b}} \left({x}\right)\right){dx}\: \\ $$$$\:\:\:\:\:\:\overset{???} {=}\:\:\:\frac{\psi\left(\frac{{b}+\mathrm{1}}{\mathrm{2}}\right)−\psi\left(\frac{{a}+\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970}…
Question Number 50384 by prof Abdo imad last updated on 16/Dec/18 $${find}\:\int\:\:\:\frac{{dx}}{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\left(\mathrm{1}−{x}^{\mathrm{3}} \right)} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{2}} ^{\sqrt{\mathrm{5}}} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\left(\mathrm{1}−{x}^{\mathrm{3}} \right)} \\ $$ Commented by Abdo…
Question Number 115896 by bemath last updated on 29/Sep/20 $$\:\int\:\frac{\mathrm{sec}\:^{\mathrm{4}} {x}\:{dx}}{\:\sqrt{\mathrm{tan}\:^{\mathrm{3}} {x}}}\:=? \\ $$ Answered by TANMAY PANACEA last updated on 29/Sep/20 $$\int\frac{\left(\mathrm{1}+{t}^{\mathrm{2}} \right){dt}}{{t}^{\frac{\mathrm{3}}{\mathrm{2}}} }\:\:\:\:\left[{t}={tanx}\:\:\:\:\:\:\frac{{dt}}{{dx}}={sec}^{\mathrm{2}}…
Question Number 181403 by a.lgnaoui last updated on 24/Nov/22 $${Refer}\:{to}\:\mathrm{Q181319} \\ $$$$\int\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{4}} +{x}+\mathrm{2}}{dx} \\ $$$$\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{4}} +{x}+\mathrm{2}}=\mathrm{1}+\frac{{x}}{\mathrm{2}\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)}−\frac{{x}}{\mathrm{2}\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)} \\ $$$$=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}\left[\frac{\left(\mathrm{2}{x}+\mathrm{1}\right)−\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{4}}×\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)+\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)}\right. \\…
Question Number 181319 by a.lgnaoui last updated on 23/Nov/22 $${Determiner} \\ $$$$\mathrm{1}.\:\:\:\int\frac{{x}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$$$\mathrm{2}.\:\:\:\int\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Answered by floor(10²Eta[1]) last…
Question Number 115781 by bemath last updated on 28/Sep/20 $$\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}} {\int}}\:\frac{{x}\:\mathrm{sin}^{−\mathrm{1}} \left({x}^{\mathrm{2}} \right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }}\:{dx}\:=? \\ $$$$\int\mathrm{2}^{−{x}} \:\mathrm{tanh}\:\left(\mathrm{2}^{\mathrm{1}−{x}} \right)\:{dx}\:=? \\ $$ Answered by bobhans last…
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}}…