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Category: Integration

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}}…

Question-152147

Question Number 152147 by john_santu last updated on 26/Aug/21 Answered by Ar Brandon last updated on 26/Aug/21 $${I}_{{n}} =\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\sqrt{{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{n}}}−\mid{x}\mid\right){dx} \\ $$$$\:\:\:\:=\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}}…