Question Number 121860 by Bird last updated on 12/Nov/20 $${calculate}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\frac{{arctan}\left(\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right)}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{dxdy} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 121858 by Bird last updated on 12/Nov/20 $${decompose}\:{F}\left({x}\right)\:=\frac{{x}^{{n}} }{{x}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{1}} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{{n}} }{{x}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{1}}{dx} \\ $$$${n}\:{integr}\:{natural} \\ $$ Terms of Service…
Question Number 121859 by Bird last updated on 12/Nov/20 $${find}\:\int\:\:\:\frac{{dx}}{\left({x}−\mathrm{1}\right)\sqrt{{x}+\mathrm{1}}−\left({x}+\mathrm{1}\right)\sqrt{{x}−\mathrm{1}}} \\ $$ Answered by ajfour last updated on 12/Nov/20 $${I}=\int\frac{\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}}{\:\sqrt{{x}−\mathrm{1}}−\sqrt{{x}+\mathrm{1}}} \\ $$$$ \\ $$$$\:\:=\int\:\frac{\left(\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}\right){dx}}{\mathrm{2}\sqrt{{x}^{\mathrm{2}}…
Question Number 121857 by Bird last updated on 12/Nov/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{xe}^{−{x}^{\mathrm{2}} } {arctan}\left(\mathrm{2}{x}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 121854 by abdelsalamalmukasabe last updated on 12/Nov/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 56311 by maxmathsup by imad last updated on 13/Mar/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({xt}\right)}{{x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} }\:{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({t}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left(\mathrm{2}{t}\right)}{\mathrm{4}+{t}^{\mathrm{2}}…
Question Number 56310 by maxmathsup by imad last updated on 13/Mar/19 $${let}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\:{cos}\left({t}^{\mathrm{2}} \:+{xt}\:+\mathrm{3}\right){dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{1}} ^{\mathrm{4}} {f}\left({x}\right){dx}\:{and}\:\int_{\mathrm{1}} ^{+\infty} {f}\left({x}\right){dx} \\ $$…
Question Number 187374 by ajfour last updated on 16/Feb/23 $$\int\sqrt{\frac{{t}+\mathrm{1}}{{t}\left({k}−{t}\right)}}{dt}=? \\ $$ Commented by ajfour last updated on 16/Feb/23 $${see}\:{Q}.\mathrm{187364} \\ $$ Commented by MJS_new…
Question Number 121825 by bemath last updated on 12/Nov/20 $$\:\:\int\:\frac{{dx}}{{x}−\mathrm{4}\sqrt{{x}}}\:? \\ $$ Commented by bemath last updated on 12/Nov/20 $$\:\int\:\frac{{dx}}{\:\sqrt{{x}}\:\left(\sqrt{{x}}−\mathrm{4}\right)}\:{dx}\:=\:\mathrm{2}\int\:\frac{{d}\left(\sqrt{{x}}−\mathrm{4}\right)}{\:\sqrt{{x}}−\mathrm{4}} \\ $$$$=\:\mathrm{2}\:\mathrm{ln}\:\mid\sqrt{{x}}−\mathrm{4}\:\mid\:+\:{c}\: \\ $$ Answered…
Question Number 121814 by bemath last updated on 12/Nov/20 Terms of Service Privacy Policy Contact: info@tinkutara.com