Category: Integration

Question Number 70686 by mathmax by abdo last updated on 06/Oct/19 $$find\int \frac{dx}{1+x^6}$$ Answered by kaivan.ahmadi last updated on 06/Oct/19 Answered by MJS…

Question Number 136210 by Ar Brandon last updated on 19/Mar/21 $$\mathrm{Show}\mathrm{that}{\int }_0^{\mathrm{\infty }}\frac{\mathrm{lnx}}{{({\mathrm{x}}^2+1)}^2}\mathrm{dx}=-\frac{\pi }{4}$$ Commented by Ar Brandon last updated on 19/Mar/21…

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 70602 by oyemi kemewari last updated on 06/Oct/19 $$\mathrm{I}={\int }_0^{\mathrm{\infty }}\ln (\sqrt{1-\mathrm{x}}+\sqrt{1+\mathrm{x}})\mathrm{dx}$$ 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 136132 by frc2crc last updated on 19/Mar/21 $$Findaseriesfor\frac{x^2}{\tanh \left(x\pi \right)\tan \left(x\pi \right)}$$ 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}}…