Question Number 223079 by Nicholas666 last updated on 14/Jul/25 $$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\boldsymbol{\mathrm{Evaluate}}\::\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{arctan}\left({x}\right)}{{x}}\:\mathrm{Li}_{\mathrm{2}} \left({x}\right)\:\mathrm{d}{x} \\ $$$$ \\ $$ Answered by MrGaster last updated on…
Question Number 223034 by MrGaster last updated on 13/Jul/25 $$ \\ $$$$\int\frac{{x}\:\mathrm{arctan}{xdx}}{\:\sqrt{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{k}'^{\mathrm{2}} {x}^{\mathrm{2}} \right)}}=\frac{\mathrm{1}}{{k}^{\mathrm{2}} }\left[{F}\left(\frac{\pi}{\mathrm{4}},{k}\right)−\frac{\pi}{\mathrm{2}\sqrt{\mathrm{2}\left(\mathrm{1}+{k}'\mathrm{2}\right)}}\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 223040 by MrGaster last updated on 13/Jul/25 Commented by Nicholas666 last updated on 14/Jul/25 $$\:\:\mathrm{thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{sir},\: \\ $$$$\:\mathrm{very}\:\mathrm{nice}\:\mathrm{you}'\mathrm{re}\:\mathrm{approach}\:\:\:\mathrm{solution}\:\mathrm{to}\:\mathrm{this}\:\mathrm{problem}\: \\ $$$$ \\ $$ Terms of…
Question Number 223007 by Nicholas666 last updated on 12/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\mathrm{everyone}\:\mathrm{or}\:\mathrm{Mr}.\:\mathrm{Gaster}\:! \\ $$$$\:\:\:\:\:\:\:\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to}\:\mathrm{sove}\:\mathrm{the}\:\mathrm{integral}\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Because}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{is}\:\mathrm{very}\:\mathrm{crazy}\:\mathrm{or}\:\mathrm{very}\:\mathrm{Complicated} \\ $$$$\:\:\:\:\:\:\mathrm{Problem}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{ln}\left({x}−\mathrm{1}\right)\:\mathrm{ln}\left({x}+\mathrm{1}\right)\:\mathrm{ln}\:\left({x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:\mathrm{d}{x}\:=??? \\…
Question Number 222996 by MrGaster last updated on 12/Jul/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{2}−{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} {dx} \\ $$ Answered by MrGaster last updated on 12/Jul/25 Answered by…
Question Number 222993 by dr1001sa last updated on 12/Jul/25 Commented by dr1001sa last updated on 12/Jul/25 $${help},{please} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 222927 by MrGaster last updated on 11/Jul/25 $$\int\int\int_{{V}} \bigtriangledown\centerdot\boldsymbol{\mathrm{F}}{dV}=\int\int_{\partial{V}} \boldsymbol{\mathrm{F}}\centerdot\mathrm{d}\boldsymbol{{S}} \\ $$$$\boldsymbol{\mathrm{F}}=−\bigtriangledown\phi \\ $$$$\bigtriangledown\centerdot\left(−\bigtriangledown\phi\right)=−\bigtriangledown^{\mathrm{2}} \phi \\ $$$$\int\int\int_{{V}} \left(−\bigtriangledown^{\mathrm{2}} \phi\right){dV}=\int\int_{\partial{V}} \left(−\bigtriangledown\phi\right)\centerdot\mathrm{d}\boldsymbol{{S}} \\ $$$$−\int\int\int_{{V}} \bigtriangledown^{\mathrm{2}}…
Question Number 222908 by Nicholas666 last updated on 10/Jul/25 Answered by Ak090 last updated on 10/Jul/25 $${d}/{dx}\:{ln}\left({cosh}\:{x}\right)\:=\:{tanh}\:{x} \\ $$$${d}/{dx}\:^{{p}} \sqrt{{x}}\:\mathrm{using}\:\mathrm{the}\:\mathrm{formula}\:{d}/{dx}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$=\:\mathrm{1}/{f}'\left({f}^{−\mathrm{1}} \left({x}\right)\right)\:=\:\mathrm{1}/{px}^{\left({p}−\mathrm{1}\right)/{p}} \\…
Question Number 222876 by pranapatiaditya last updated on 10/Jul/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{2}{y}} ^{\mathrm{2}} {e}^{{x}^{\mathrm{2}} } {dxdy}=? \\ $$ Answered by MrGaster last updated on 10/Jul/25…
Question Number 222879 by MrGaster last updated on 10/Jul/25 Answered by gabthemathguy25 last updated on 10/Jul/25 $$\approx\mathrm{1}.\mathrm{67215} \\ $$ Terms of Service Privacy Policy Contact:…