Question Number 70686 by mathmax by abdo last updated on 06/Oct/19 $${find}\:\int\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{6}} } \\ $$ Answered by kaivan.ahmadi last updated on 06/Oct/19 Answered by MJS…
Question Number 136211 by greg_ed last updated on 19/Mar/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{guyz}}\:!\: \\ $$$$\boldsymbol{\mathrm{please}},\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{ur}}\:\boldsymbol{\mathrm{help}}\:! \\ $$$$\boldsymbol{\mathrm{I}}=\int_{\mathrm{1}} ^{\:\mathrm{5}} \boldsymbol{{xe}}^{\boldsymbol{{x}}^{\mathrm{3}} } \boldsymbol{{dx}} \\ $$ Answered by Olaf last updated…
Question Number 136210 by Ar Brandon last updated on 19/Mar/21 $$\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{lnx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx}=−\frac{\pi}{\mathrm{4}} \\ $$ Commented by Ar Brandon last updated on 19/Mar/21…
Question Number 136197 by Ar Brandon last updated on 19/Mar/21 $$\mathrm{a}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{real}\:\mathrm{constant}\:\mathrm{a}\:\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\frac{\mathrm{a}}{\mathrm{x}^{\mathrm{2}} }} \mathrm{dx}=\infty \\ $$$$\mathrm{b}.\:\mathrm{If}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{are}\:\mathrm{real}\:\mathrm{constants},\:\mathrm{explain}\:\mathrm{why}\:\mathrm{we}\:\mathrm{cannot}\:\mathrm{split}\:\mathrm{the} \\ $$$$\mathrm{integral}\:\:\int_{\mathrm{0}} ^{\infty} \left(\mathrm{e}^{−\frac{\mathrm{a}}{\mathrm{x}^{\mathrm{2}} }} −\mathrm{e}^{−\frac{\mathrm{b}}{\mathrm{x}^{\mathrm{2}} }} \right)\mathrm{dx}\:\mathrm{as}\:\mathrm{the}\:\mathrm{difference}\:\int_{\mathrm{0}}…
Question Number 70651 by sadimuhmud 136 last updated on 06/Oct/19 Commented by Prithwish sen last updated on 06/Oct/19 $$\mathrm{Let}\:\sqrt{\mathrm{x}}\:=\:\mathrm{u}\:\:\Rightarrow\:\mathrm{d}\left(\sqrt{\mathrm{x}}\right)=\mathrm{du} \\ $$$$\int_{\mathrm{0}} ^{\frac{\mathrm{2}}{\:\sqrt{\mathrm{a}}}} \mathrm{e}^{\sqrt{\mathrm{a}}\mathrm{u}} \mathrm{du}\:\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{a}}}\:\left[\boldsymbol{\mathrm{e}}^{\sqrt{\boldsymbol{\mathrm{a}}}\boldsymbol{\mathrm{u}}} \right]_{\mathrm{0}}…
Question Number 136170 by mnjuly1970 last updated on 19/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:{calculus}…. \\ $$$$\:\:\:{compute}:: \\ $$$$\mathrm{2}{li}_{\mathrm{2}} \left(\frac{−\mathrm{1}}{\mathrm{2}}\right)−\mathrm{2}{li}_{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)+{li}_{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)=?? \\ $$$$ \\ $$ Answered by mindispower last…
Question Number 70602 by oyemi kemewari last updated on 06/Oct/19 $$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \mathrm{ln}\left(\sqrt{\mathrm{1}−\mathrm{x}}\:+\sqrt{\mathrm{1}+\mathrm{x}}\right)\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 06/Oct/19 $${error}\:{in}\:{the}\:{question}\:{the}\:{function}\:{x}\rightarrow\sqrt{\mathrm{1}−{x}}+\sqrt{\mathrm{1}+{x}}\:{is}\:{defined}\:{on}…
Question Number 5065 by gourav~ last updated on 07/Apr/16 $$\int\sqrt{\mathrm{16}{x}^{\mathrm{2}} +\mathrm{25}}\:\:{dx}\:=? \\ $$ Answered by Yozzii last updated on 08/Apr/16 $${Let}\:{x}=\frac{\mathrm{5}}{\mathrm{4}}{sinh}\theta\Rightarrow{dx}=\frac{\mathrm{5}}{\mathrm{4}}{cosh}\theta{d}\theta \\ $$$$\sqrt{\mathrm{16}{x}^{\mathrm{2}} +\mathrm{25}}=\sqrt{\mathrm{16}×\frac{\mathrm{25}}{\mathrm{16}}{sinh}^{\mathrm{2}} \theta+\mathrm{25}}…
Question Number 136132 by frc2crc last updated on 19/Mar/21 $${Find}\:{a}\:{series}\:{for}\:\frac{{x}^{\mathrm{2}} }{\mathrm{tanh}\:\left({x}\pi\right)\mathrm{tan}\:\left({x}\pi\right)} \\ $$ Answered by Dwaipayan Shikari last updated on 19/Mar/21 $${sinh}\left(\pi{x}\right)=\pi{x}\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{{x}^{\mathrm{2}} }{{n}^{\mathrm{2}}…
Question Number 70594 by mathmax by abdo last updated on 06/Oct/19 $${calculate}\:{by}\:{residus}\:{method}\:{the}\:{integral}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} } \\ $$$${with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1} \\ $$ Commented by mathmax by abdo…