Question Number 63852 by aliesam last updated on 10/Jul/19 $${prove}\:{that} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {arctan}\left({x}\right)\:{cot}\left(\frac{\pi{x}}{\mathrm{2}}\right)\:{dx}\:=\:\frac{\mathrm{3}\:{ln}^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{2}\pi}+\frac{{ln}\pi\:{ln}\mathrm{2}}{\pi}+\int_{\mathrm{0}} ^{\infty} \frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{{e}^{\mathrm{2}\pi{x}} +\mathrm{1}}\:{dx} \\ $$ Terms of…
Question Number 63844 by mmkkmm000m last updated on 10/Jul/19 $$\int\left(\mathrm{1}+\mathrm{4}{x}+{x}^{\mathrm{2}} \right)^{{m}} {dx} \\ $$ Commented by mathmax by abdo last updated on 10/Jul/19 $${let}\:{A}_{{m}} =\int\:\left({x}^{\mathrm{2}}…
Question Number 129377 by pipin last updated on 15/Jan/21 $$\int\frac{\:\sqrt{\boldsymbol{\mathrm{x}}}}{\:\sqrt{\boldsymbol{\mathrm{x}}-\mathrm{1}}}\mathrm{dx}\:=\:… \\ $$ Answered by Ar Brandon last updated on 15/Jan/21 $$\mathcal{I}=\int\frac{\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{x}−\mathrm{1}}}\mathrm{dx}\:,\:\mathrm{x}=\mathrm{t}^{\mathrm{2}} \:\Rightarrow\mathrm{dx}=\mathrm{2tdt} \\ $$$$\:\:\:=\mathrm{2}\int\frac{\mathrm{t}^{\mathrm{2}} }{\:\sqrt{\mathrm{t}^{\mathrm{2}}…
Question Number 129370 by bramlexs22 last updated on 15/Jan/21 Answered by Ar Brandon last updated on 15/Jan/21 $$\Theta=\int_{\mathrm{1}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{y}} \frac{\mathrm{dxdy}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }=\int_{\mathrm{1}} ^{\mathrm{2}}…
Question Number 63822 by mathmax by abdo last updated on 09/Jul/19 $${find}\:\int\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{\frac{{x}+\mathrm{1}}{{x}−\mathrm{2}}}{dx} \\ $$ Commented by mathmax by abdo last updated on 11/Jul/19 $${let}\:{A}\:=\int\:\left({x}^{\mathrm{2}}…
Question Number 63823 by mathmax by abdo last updated on 09/Jul/19 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 129318 by mnjuly1970 last updated on 14/Jan/21 $$\:\:\:\:\:…\:\:{laplace}\:\:\:\:\:{transformation}.. \\ $$$$\:\:\:\:\mathscr{L}\:\:\left({te}^{−{t}} \lfloor{t}\rfloor\right)=? \\ $$$$\:\:\:{note}\::\:\lfloor{x}\rfloor\:{is}\:{floor}\:{of}\:''\:{x}\:''… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………….. \\ $$$$ \\ $$ Answered by mathmax by…
Question Number 63782 by mathmax by abdo last updated on 09/Jul/19 $${let}\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({a}^{\mathrm{2}} +{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right){calculste}\:{also}\:{g}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \right)^{\mathrm{4}}…
Question Number 63748 by aliesam last updated on 08/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 129277 by liberty last updated on 14/Jan/21 $$\:\mathrm{O}\:=\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{arctan}\:\left(\frac{\mathrm{3X}+\mathrm{3}}{\mathrm{1}−\mathrm{2X}−\mathrm{X}^{\mathrm{2}} }\right)}{\mathrm{1}+\mathrm{X}^{\mathrm{2}} }\:\mathrm{dX} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com