Menu Close

Category: Integration

x-2-1-x-2-1-1-1-x-4-dx-

Question Number 143142 by Ar Brandon last updated on 10/Jun/21 $$\int\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\centerdot\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }}\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 10/Jun/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}}…

0-1-log-1-x-x-2-x-3-x-4-1-1-x-1-x-2-1-x-3-1-x-4-dx-

Question Number 77570 by TawaTawa last updated on 08/Jan/20 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\:\mathrm{log}\left(\frac{\mathrm{1}\:+\:\mathrm{x}\:+\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{4}} }{\:\sqrt{\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }}}\right)\:\mathrm{dx} \\ $$ Answered by MJS last updated…

Prove-n-1-1-sinh-pin-2-1-6-1-2pi-

Question Number 143098 by mnjuly1970 last updated on 10/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{Prove}….\: \\ $$$$\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{s}{inh}\left(\pi{n}\right)}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{6}}\:−\frac{\mathrm{1}}{\mathrm{2}\pi}\:\:\:… \\ $$$$\:\:\:\:\:\:\:…… \\ $$ Answered by Dwaipayan Shikari…

x-2-x-2-x-1-dx-

Question Number 77552 by lémùst last updated on 07/Jan/20 $$\int\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}\:=\:? \\ $$ Answered by MJS last updated on 07/Jan/20 $$\int\frac{{x}−\mathrm{2}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}−\mathrm{4}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}−\mathrm{1}}{{x}^{\mathrm{2}}…

Question-143087

Question Number 143087 by bramlexs22 last updated on 10/Jun/21 Answered by Ar Brandon last updated on 10/Jun/21 $$\mathrm{x}=\mathrm{sec}\vartheta \\ $$$$\mathrm{I}=\int_{\frac{\mathrm{2}\pi}{\mathrm{3}}} ^{\frac{\mathrm{5}\pi}{\mathrm{6}}} \frac{\mathrm{sec}\vartheta\mathrm{tan}\vartheta}{\mathrm{sec}\vartheta\sqrt{\mathrm{sec}^{\mathrm{2}} \vartheta−\mathrm{1}}}\mathrm{d}\vartheta=\int_{\frac{\mathrm{2}\pi}{\mathrm{3}}} ^{\frac{\mathrm{5}\pi}{\mathrm{6}}} \frac{\mathrm{tan}\vartheta}{\:\sqrt{\mathrm{tan}^{\mathrm{2}}…