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Category: Integration

mathematical-analysis-prove-that-0-sin-3-x-x-3-dx-3pi-8-

Question Number 132987 by mnjuly1970 last updated on 17/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….{mathematical}\:\:{analysis}… \\ $$$$\:{prove}\:\:{that}::\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{3}} }{dx}=\frac{\mathrm{3}\pi}{\mathrm{8}} \\ $$$$\:\:\:\:\ast\ast\ast\ast………. \\ $$$$ \\ $$ Answered by Dwaipayan…

find-1-1-x-2-arctan-1-1-x-dx-

Question Number 67374 by mathmax by abdo last updated on 26/Aug/19 $${find}\:\int\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctan}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right){dx} \\ $$ Commented by Abdo msup. last updated on 27/Aug/19 $${let}\:{I}\:=\int\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arcran}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right){dx}\:{by}\:{psrts}…