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Category: Integration

x-sin-1-x-dx-

Question Number 84666 by jagoll last updated on 14/Mar/20 $$\int\:{x}\:\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\:{dx}\: \\ $$ Commented by mathmax by abdo last updated on 15/Mar/20 $${A}\:=\int\:{xarcsinx}\:{dx}\:\:{by}\:{parts}\:\:{u}^{'} ={x}\:{and}\:{v}={arcsinx}\:\Rightarrow \\…

sec-3-x-dx-

Question Number 19077 by Joel577 last updated on 04/Aug/17 $$\int\:\mathrm{sec}^{\mathrm{3}} \:{x}\:{dx} \\ $$ Answered by ajfour last updated on 04/Aug/17 $$\mathrm{I}=\int\mathrm{sec}\:\theta\left(\mathrm{sec}\:^{\mathrm{2}} \theta\mathrm{d}\theta\right) \\ $$$$=\mathrm{sec}\:\theta\int\mathrm{sec}\:^{\mathrm{2}} \theta\mathrm{d}\theta−\int\left[\frac{\mathrm{d}}{\mathrm{d}\theta}\left(\mathrm{sec}\:\theta\right).\int\mathrm{sec}\:^{\mathrm{2}}…

calculate-dx-cosx-cos-2x-cos-3x-

Question Number 84577 by msup trace by abdo last updated on 14/Mar/20 $${calculate}\:\int\:\:\:\:\frac{{dx}}{{cosx}\:+{cos}\left(\mathrm{2}{x}\right)+{cos}\left(\mathrm{3}{x}\right)} \\ $$ Commented by jagoll last updated on 14/Mar/20 $$\mathrm{cos}\:{x}+\mathrm{cos}\:\mathrm{3}{x}+\mathrm{cos}\:\mathrm{2}{x}\:=\: \\ $$$$\mathrm{2cos}\:\mathrm{2}{x}\:\mathrm{cos}\:{x}\:+\:\mathrm{cos}\:\mathrm{2}{x}\:=\:…