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Category: Integration

cos-log-x-dx-

Question Number 152161 by peter frank last updated on 26/Aug/21 $$\int\mathrm{cos}\:\left(\mathrm{log}\:\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 26/Aug/21 $$\mathrm{F}\left({x}\right)\:=\:\int\mathrm{cos}\left(\mathrm{log}{x}\right)\:{dx} \\ $$$$\mathrm{F}\left({e}^{{u}} \right)\:=\:\int\mathrm{cos}{u}\:{e}^{{u}} {du}…

Question-86627

Question Number 86627 by Omer Alattas last updated on 29/Mar/20 Commented by abdomathmax last updated on 29/Mar/20 $${x}\rightarrow\frac{{tanx}}{\mathrm{1}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} }\:{is}\:{odd}\:\Rightarrow\int_{−\mathrm{1}} ^{\mathrm{1}} \:\frac{{tanx}}{\mathrm{1}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} }{dx}=\mathrm{0} \\…

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

Question Number 152160 by peter frank last updated on 26/Aug/21 $$\int\left[\frac{\mathrm{1}}{\mathrm{log}\:\mathrm{x}}−\frac{\mathrm{1}}{\left(\mathrm{log}\:\mathrm{x}\right)^{\mathrm{2}} }\right]\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 26/Aug/21 $$\mathrm{F}\left({x}\right)\:=\:\int\left(\frac{\mathrm{1}}{\mathrm{log}{x}}−\frac{\mathrm{1}}{\mathrm{log}^{\mathrm{2}} {x}}\right){dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:\int\frac{\mathrm{log}{x}−\mathrm{1}}{\mathrm{log}^{\mathrm{2}}…

tan-x-dx-

Question Number 86615 by ar247 last updated on 29/Mar/20 $$\int\sqrt{{tan}\:{x}\:}{dx} \\ $$ Commented by Ar Brandon last updated on 29/Mar/20 $${let}\:\:{t}^{\mathrm{2}} ={tan}\:{x}\:\:\Rightarrow\mathrm{2}{tdt}={sec}^{\mathrm{2}} {xdx} \\ $$$$\Rightarrow{dx}=\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{4}}…