Question Number 59050 by maxmathsup by imad last updated on 04/May/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\: \\ $$ Answered by tanmay last updated on 04/May/19…
Question Number 124587 by mnjuly1970 last updated on 04/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\blacktriangleleft::::\blacktriangleright\:{calculus} \\ $$$$\:\:\:\:\:{simple}\:\:{question}:: \\ $$$$\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{4}}{\:\sqrt{\mathrm{4}+{x}^{\mathrm{4}} }}\:{dx}\overset{???} {=}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\:\sqrt{{sin}\left({x}\right)}}\:+\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\:\sqrt{{cos}\left({x}\right)}} \\…
Question Number 124579 by bemath last updated on 04/Dec/20 $$\:\:{I}=\int_{\mathrm{0}} ^{\:\infty} \:\frac{{dx}}{\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{2}} }\:? \\ $$ Answered by liberty last updated on 04/Dec/20 $${I}=\int_{\:\mathrm{0}} ^{\:\infty}…
Question Number 59040 by rahul 19 last updated on 03/May/19 $$\left.\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:^{\mathrm{4}} {x}}{dx}\:=\:? \\ $$ Answered by tanmay last updated on 03/May/19 $$\left.\mathrm{1}\right)\int\frac{{sinxdx}}{{cos}^{\mathrm{2}}…
Question Number 124566 by bemath last updated on 04/Dec/20 $$\:\int\:\frac{{dx}}{\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{2}} }\: \\ $$ Answered by liberty last updated on 05/Dec/20 $$\:\int\:\frac{{dx}}{\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{2}} }\:=\:? \\…
Question Number 59012 by cesar.marval.larez@gmail.com last updated on 03/May/19 Answered by tanmay last updated on 03/May/19 $$\left.\mathrm{182}\right)\int\frac{\mathrm{2}{x}−\mathrm{7}}{{x}^{\mathrm{2}} +\mathrm{9}}{dx} \\ $$$$\int\frac{{d}\left({x}^{\mathrm{2}} +\mathrm{9}\right)}{{x}^{\mathrm{2}} +\mathrm{9}}−\mathrm{7}\int\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} } \\…
Question Number 124542 by micelle last updated on 04/Dec/20 $${help}\:\:\int\mathrm{3}{xdx} \\ $$ Commented by bemath last updated on 04/Dec/20 $$\int\:\mathrm{3}{x}\:{dx}\:=\:\frac{\mathrm{6}}{\mathrm{2}}\int\:{x}\:{dx}\:=\:\frac{\mathrm{9}}{\mathrm{3}}\int{x}\:{dx}\: \\ $$$$\:=\:\frac{\mathrm{6}{x}^{\mathrm{2}} }{\mathrm{4}}+{c}\:=\:\frac{\mathrm{9}{x}^{\mathrm{2}} }{\mathrm{6}}+{c}\: \\…
Question Number 124540 by micelle last updated on 04/Dec/20 $$\int\frac{\mathrm{4}{x}+\mathrm{9}}{{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{10}}{dx} \\ $$ Answered by Ar Brandon last updated on 04/Dec/20 $$\mathcal{I}=\int\frac{\mathrm{4x}+\mathrm{9}}{\mathrm{x}^{\mathrm{2}} +\mathrm{6x}+\mathrm{10}}\mathrm{dx} \\ $$$$\mathrm{4x}+\mathrm{9}=\lambda\left\{\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}^{\mathrm{2}}…
Question Number 124530 by Bird last updated on 03/Dec/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{{n}} \right){dx}\:{snd}\:\int_{\mathrm{0}} ^{\infty} {sin}\left({x}^{{n}} \right){dx} \\ $$ Commented by Dwaipayan Shikari last updated on…
Question Number 124532 by liberty last updated on 04/Dec/20 $$\:\int\:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:? \\ $$ Answered by bemath last updated on 04/Dec/20 $$\:\vartheta\left({x}\right)\:=\:\int\:\frac{{dx}}{{x}^{\mathrm{3}} \:\sqrt{\mathrm{1}−{x}^{−\mathrm{2}} }}\:=\:\int\:\frac{{x}^{−\mathrm{3}} }{\:\sqrt{\mathrm{1}−{x}^{−\mathrm{2}}…