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Category: Integration

dx-x-4-1-3-

Question Number 86871 by john santu last updated on 01/Apr/20 $$\int\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated on 01/Apr/20 $${complex}\:{method}\:{I}\:=\int\:\:\frac{{dx}}{\left({x}^{\mathrm{4}}…

prove-S-n-1-1-1-3-2pi-3-27-

Question Number 152345 by mnjuly1970 last updated on 27/Aug/21 $$ \\ $$$$\:\:\:\:{prove}… \\ $$$$\:\:\:\:\:\mathrm{S}\:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:+\frac{\mathrm{2}\pi\:\sqrt{\mathrm{3}}}{\mathrm{27}}\:…\blacksquare \\ $$$$ \\ $$ Answered by Kamel last updated…

dx-cos-x-cosec-x-

Question Number 152291 by iloveisrael last updated on 27/Aug/21 $$\:\int\:\frac{{dx}}{\mathrm{cos}\:{x}+\mathrm{cosec}\:{x}}\:=? \\ $$ Answered by puissant last updated on 27/Aug/21 $${I}=\int\frac{{dx}}{{cosx}+{cosecx}} \\ $$$$=\int\frac{{sinx}}{{cosxsinx}+\mathrm{1}}{dx}\:=\:\int\frac{\mathrm{2}{sinx}}{{sin}\mathrm{2}{x}+\mathrm{2}}{dx} \\ $$$$=\int\frac{{sinx}+{cosx}}{{sin}\mathrm{2}{x}+\mathrm{2}}{dx}+\int\frac{{sinx}−{cosx}}{{sin}\mathrm{2}{x}+\mathrm{2}}{dx} \\…