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Question Number 110301 by Lekhraj last updated on 28/Aug/20 Commented by mathmax by abdo last updated on 28/Aug/20 $$\mathrm{this}\:\mathrm{integral}\:\mathrm{is}\:\mathrm{divergent}…! \\ $$ Terms of Service Privacy…
Question Number 110262 by Ar Brandon last updated on 28/Aug/20 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{X}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right),\:\mathrm{Y}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right),\:\mathrm{Z}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right) \\ $$$$\begin{cases}{\frac{\partial\mathrm{Z}}{\partial\mathrm{y}}−\frac{\partial\mathrm{Y}}{\partial\mathrm{z}}=\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\\{\frac{\partial\mathrm{Z}}{\partial\mathrm{x}}−\frac{\partial\mathrm{X}}{\partial\mathrm{z}}=−\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{2}}}\\{\frac{\partial\mathrm{Y}}{\partial\mathrm{x}}−\frac{\partial\mathrm{X}}{\partial\mathrm{y}}=\mathrm{z}\left(\mathrm{2x}−\mathrm{y}\right)}\end{cases}\:\mathrm{where}\:\begin{cases}{\mathrm{X}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\\{\mathrm{Y}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\\{\mathrm{Z}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\end{cases} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 44712 by peter frank last updated on 03/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 03/Oct/18 $$\left.\mathrm{1}\right)\int\frac{{x}^{{n}−\mathrm{1}} }{{x}^{{n}} \left(\mathrm{1}+{x}^{{n}} \right)}{dx} \\ $$$${t}={x}^{{n}} \:\:\:{dt}={nx}^{{n}−\mathrm{1}} {dx}…
Question Number 110245 by Her_Majesty last updated on 28/Aug/20 $${solve}\:\int\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{{c}−\sqrt{{b}−{ax}}}} \\ $$ Commented by Lordose last updated on 28/Aug/20 $$\int\frac{\boldsymbol{\mathrm{dx}}}{\:\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{c}}−\sqrt{\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{ax}}}}} \\ $$$$\bigstar\boldsymbol{\mathrm{Solution}} \\ $$$$\boldsymbol{\mathrm{set}}\:\boldsymbol{\mathrm{u}}=\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{ax}} \\…
Question Number 110247 by Rio Michael last updated on 28/Aug/20 $$\mathrm{Let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\:{x}} {e}^{−{t}} {dt}\: \\ $$$$\mathrm{then}\:{f}\:''\left({x}\right)\:=\:?? \\ $$ Answered by bemath last updated on 28/Aug/20…
Question Number 44706 by maxmathsup by imad last updated on 03/Oct/18 $${let}\:{f}_{\alpha} \left({x}\right)\:=\:\frac{{cos}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{give}\:\int_{\mathrm{0}} ^{{x}} \:{f}_{\alpha} \left({t}\right)\:{dt}\:\:{at}\:{form}\:{of}\:{serie}\:…
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Question Number 44697 by manish09@gmail.com last updated on 03/Oct/18 $$\boldsymbol{{prove}}\:\boldsymbol{{that}}:− \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{t}}^{\boldsymbol{{a}}−\mathrm{1}} }{\mathrm{1}+\boldsymbol{{t}}}\boldsymbol{{dt}}\:=\:\frac{\boldsymbol{\pi}}{\boldsymbol{{sin}}\left(\boldsymbol{\pi{a}}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 44696 by manish09@gmail.com last updated on 03/Oct/18 $$\int\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{4}} }\boldsymbol{\mathrm{dx}}\:=\:? \\ $$ Commented by maxmathsup by imad last updated on 03/Oct/18 $${let}\:{decompose}\:{F}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} } \\…