Menu Close

Category: Integration

1-ln-x-dx-

Question Number 132110 by Raxreedoroid last updated on 11/Feb/21 $$\int\frac{\mathrm{1}}{\mathrm{ln}\:{x}}{dx}=? \\ $$ Answered by Olaf last updated on 11/Feb/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{{dx}}{\mathrm{ln}{x}} \\ $$$$\mathrm{Let}\:{x}\:=\:{e}^{{u}} \\ $$$$\mathrm{F}\left({e}^{{u}} \right)\:=\:\int\frac{{d}\left({e}^{{u}}…

evaluate-0-2-x-2-dx-

Question Number 66561 by Rio Michael last updated on 17/Aug/19 $${evaluate}\: \\ $$$$\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \mid\:{x}+\:\mathrm{2}\mid\:{dx}. \\ $$ Commented by kaivan.ahmadi last updated on 17/Aug/19 $$\mathrm{0}<{x}<\mathrm{2}\Rightarrow{x}+\mathrm{2}>\mathrm{0}\Rightarrow\mid{x}+\mathrm{2}\mid={x}+\mathrm{2}…

Solve-dx-1-x-2-3-

Question Number 132082 by liberty last updated on 11/Feb/21 $$\:\mathrm{Solve}\:\int\:\frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:?\: \\ $$ Answered by EDWIN88 last updated on 11/Feb/21 $$\mathrm{Ostrogradski}\:\mathrm{method} \\ $$$$\mathrm{Consider}\:\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{ax}^{\mathrm{3}} +\mathrm{bx}}{\left(\mathrm{x}^{\mathrm{2}}…