Question Number 29854 by abdo imad last updated on 13/Feb/18 $${find}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\:\:\frac{\left({x}^{\mathrm{2}} +\mathrm{2}\right){dx}}{{x}^{\mathrm{4}} \:+\mathrm{8}{x}^{\mathrm{2}} −\mathrm{16}{x}\:+\mathrm{20}}\:. \\ $$ Commented by abdo imad last updated on…
Question Number 29852 by abdo imad last updated on 13/Feb/18 $${let}\:{f}\left({z}\right)\:={z}\:{cos}^{\mathrm{2}} \left(\frac{\pi}{{z}}\right)\:\:{find}\:{Res}\left({f},\mathrm{0}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 29853 by abdo imad last updated on 13/Feb/18 $${find}\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{ix}\:+\mathrm{2}−\mathrm{4}{i}}\:. \\ $$ Commented by abdo imad last updated on 18/Feb/18 $${let}\:{put}\:{f}\left({z}\right)=\:\frac{\mathrm{1}}{{z}^{\mathrm{2}}…
Question Number 29850 by abdo imad last updated on 13/Feb/18 $${find}\:\:{I}\:\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} \:\:−\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} }{{x}}{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 29849 by abdo imad last updated on 12/Feb/18 $${let}\:{give}\:{a}>\mathrm{0}\:,{b}>\mathrm{0}\:{find}\:{the}\:{vslue}\:{of}\: \\ $$$$\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{e}^{−{at}} \:−{e}^{−{bt}} }{{t}}\:{cos}\left({xt}\right){dt}\:. \\ $$ Commented by abdo imad last updated…
Question Number 95371 by Fikret last updated on 24/May/20 $$\int\frac{{x}^{\mathrm{2}/\mathrm{3}} }{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}/\mathrm{3}} }}{dx}=? \\ $$ Commented by bobhans last updated on 25/May/20 $$\int\:\frac{\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{1}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}^{\mathrm{2}} }}}\:\mathrm{dx}\:.\:\mathrm{let}\:\sqrt{\mathrm{1}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}^{\mathrm{2}} }}\:=\:\mathrm{t}…
Question Number 160902 by blackmamba last updated on 08/Dec/21 $$\:\:\int\:\frac{{dx}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{3}} {x}}\:\sqrt{\mathrm{cos}\:^{\mathrm{5}} {x}}}\:=? \\ $$ Answered by chhaythean last updated on 09/Dec/21 $$=\int\frac{\mathrm{dx}}{\:\sqrt{\frac{\mathrm{sin}^{\mathrm{3}} \mathrm{x}}{\mathrm{cos}^{\mathrm{3}} \mathrm{x}}×\mathrm{cos}^{\mathrm{8}} \mathrm{x}}}…
Question Number 160807 by ArielVyny last updated on 07/Dec/21 $$−\mathrm{1}\leqslant{a}_{\mathrm{0}} \leqslant{b}_{\mathrm{0}} \leqslant{c}_{\mathrm{0}} \leqslant\mathrm{1} \\ $$$$\forall{n}\in\mathbb{N}\: \\ $$$${a}_{{n}+\mathrm{1}} =\int_{−\mathrm{1}} ^{\mathrm{1}} {min}\left({x},{b}_{{n}} ,{c}_{{n}} \right){dx} \\ $$$${b}_{{n}+\mathrm{1}} =\int_{−\mathrm{1}}…
Question Number 160792 by cortano last updated on 06/Dec/21 $$\:\:\:\int\:\frac{\mathrm{sec}\:\mathrm{x}}{\:\sqrt{\mathrm{1}+\mathrm{2sec}\:\mathrm{x}}}\:\sqrt{\frac{\mathrm{cosec}\:\mathrm{x}−\mathrm{cot}\:\mathrm{x}}{\mathrm{cosec}\:\mathrm{x}+\mathrm{cot}\:\mathrm{x}}}\:\mathrm{dx}\:=? \\ $$ Answered by chhaythean last updated on 06/Dec/21 $$=\int\frac{\frac{\mathrm{1}}{\mathrm{cosx}}}{\:\sqrt{\frac{\mathrm{cosx}+\mathrm{2}}{\mathrm{cosx}}}}×\sqrt{\frac{\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{sinx}}}{\frac{\mathrm{1}+\mathrm{cosx}}{\mathrm{sinx}}}}\mathrm{dx} \\ $$$$=\int\frac{\frac{\mathrm{1}}{\mathrm{cosx}}}{\:\sqrt{\frac{\mathrm{cosx}+\mathrm{2}}{\mathrm{cosx}}}}×\sqrt{\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{1}+\mathrm{cosx}}}\mathrm{dx} \\ $$$$=\int\frac{\mathrm{sinx}}{\:\sqrt{\mathrm{cos}^{\mathrm{2}} \mathrm{x}+\mathrm{2cosx}}}×\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cosx}}\mathrm{dx}…
Question Number 160767 by cortano last updated on 06/Dec/21 $$\:\:\:\:\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx}\:=?\: \\ $$ Answered by MJS_new last updated on 06/Dec/21 $$\underset{\mathrm{0}}…