Category: Integration

Question Number 28033 by abdo imad last updated on 18/Jan/18 $$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{2}\right)\:\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xln}\left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:. \\ $$ Commented by abdo…

Question Number 159080 by qaz last updated on 12/Nov/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}!\left(\mathrm{n}^{\mathrm{4}} +\mathrm{n}^{\mathrm{2}} +\mathrm{1}\right)}=? \\ $$ Answered by mindispower last updated on 13/Nov/21 $$=\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{1}}{{n}!\left({n}^{\mathrm{2}}…

Question Number 27999 by abdo imad last updated on 18/Jan/18 $${find}\:\:{I}_{{n},{m}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \:\left(\mathrm{1}−{x}\right)^{{m}} \:{dx}\:{with} \\ $$$$\left({n},{m}\right)\in{N}^{\bigstar^{\mathrm{2}} } \:{and}\:{calculate}\:\:\sum_{{n}=\mathrm{0}} ^{\propto} \:{I}_{{n},{m}} . \\ $$…

Question Number 27974 by abdo imad last updated on 18/Jan/18 $${let}\:{put}\:{f}\left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{ax}} \:−\:{e}^{−{bx}} }{{x}^{\mathrm{2}} }\:{e}^{−{tx}^{\mathrm{2}} } \:{dx} \\ $$$${with}\:{t}\geqslant\mathrm{0}\:\:{and}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$$${find}\:{a}\:{integral}\:{form}\:{of}\:{f}\left({t}\right). \\ $$ Commented…

Question Number 27951 by tawa tawa last updated on 17/Jan/18 $$\mathrm{Use}\:\mathrm{the}\:\mathrm{trapezoidal}\:\mathrm{rule}\:\mathrm{with}\:\mathrm{5}\:\mathrm{ordinates}\:\mathrm{to}\:\mathrm{evaluate}\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{0}.\mathrm{8}} \:\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \:\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com