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Category: Integration

tan-x-cot-x-dx-

Question Number 94662 by i jagooll last updated on 20/May/20 $$\int\:\sqrt{\mathrm{tan}\:\mathrm{x}+\mathrm{cot}\:\mathrm{x}}\:\mathrm{dx}\:=\:? \\ $$ Commented by i jagooll last updated on 20/May/20 $$\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}}{\:\sqrt{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:.\sqrt{\mathrm{tan}\:\mathrm{x}}}\:=\: \\…

Show-that-1-1-dx-5-cosh-x-13-sinh-x-1-2-log-e-15e-10-3e-2-

Question Number 29105 by tawa tawa last updated on 04/Feb/18 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\int_{−\mathrm{1}} ^{\:\:\:\mathrm{1}} \:\:\:\:\:\:\:\frac{\mathrm{dx}}{\mathrm{5}\:\mathrm{cosh}\left(\mathrm{x}\right)\:+\:\mathrm{13}\:\mathrm{sinh}\left(\mathrm{x}\right)}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{log}_{\mathrm{e}} \left(\frac{\mathrm{15e}\:−\:\mathrm{10}}{\mathrm{3e}\:+\:\mathrm{2}}\right)\: \\ $$ Commented by abdo imad last updated on 04/Feb/18 $${I}=\:\int_{−\mathrm{1}}…

let-give-g-x-0-arctan-x-1-t-2-1-t-2-dt-find-a-simple-form-of-g-x-without-integral-

Question Number 29077 by abdo imad last updated on 04/Feb/18 $${let}\:{give}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:\:{find}\:{a}\:{simple} \\ $$$${form}\:{of}\:\:{g}^{'} \left({x}\right)\:{without}\:{integral}. \\ $$ Commented by abdo imad last…

let-give-f-x-0-1-arctan-x-1-t-2-1-t-2-dt-find-asimple-form-of-f-x-without-integral-

Question Number 29076 by abdo imad last updated on 04/Feb/18 $${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left({x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:\:{find}\:{asimple} \\ $$$${form}\:{of}\:{f}\left({x}\right)\:{without}\:{integral}. \\ $$ Commented by abdo imad last updated…