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 159070 by mnjuly1970 last updated on 12/Nov/21 $$ \\ $$$$ \\ $$$$\:\:\:\:\Omega:=\:\int_{\mathrm{0}} ^{\:\infty} \left(\:\mathrm{H}_{\:\frac{{i}}{{x}}} \:+\:\mathrm{H}_{\:−\frac{{i}}{{x}}} \:\right)\:{dx}=? \\ $$$$ \\ $$ Answered by mindispower…
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 27950 by tawa tawa last updated on 17/Jan/18 $$\mathrm{Find}\:\mathrm{by}\:\mathrm{the}\:\mathrm{trapezoidal}\:\mathrm{rule}\:\mathrm{the}\:\mathrm{approximate}\:\mathrm{value}\:\mathrm{of}\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{dx}}{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} }.\:\:\:\mathrm{Use} \\ $$$$\mathrm{ordinates}\:\mathrm{spaced}\:\mathrm{at}\:\mathrm{equal}\:\mathrm{interval}\:\mathrm{of}\:\mathrm{width}\:\:\mathrm{h}\:=\:\mathrm{0}.\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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
Question Number 93484 by mashallah last updated on 13/May/20 $$\int\mathrm{t}^{\mathrm{2}} /\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}} \right)^{\mathrm{2}} \mathrm{dx}= \\ $$ Commented by prakash jain last updated on 13/May/20 $$\mathrm{function}\:\mathrm{is}\:\mathrm{in}\:{t}\:\mathrm{so}\:\mathrm{constant}\:\mathrm{wrt}\:{x} \\…
Question Number 93481 by mashallah last updated on 13/May/20 $$\int\left(\mathrm{log}\:\mathrm{x}/\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}= \\ $$ Commented by abdomathmax last updated on 15/May/20 $${I}\:=\int\:\frac{{lnx}}{{x}^{\mathrm{2}} }{dx}\:\:{by}\:{parts} \\ $$$${I}\:=−\frac{{lnx}}{{x}}\:−\int\:\left(−\frac{\mathrm{1}}{{x}}\right)×\frac{{dx}}{{x}}\:=−\frac{{lnx}}{{x}}\:+\int\:\frac{{dx}}{{x}^{\mathrm{2}} }…
Question Number 159008 by amin96 last updated on 11/Nov/21 $$\int\frac{\mathrm{6}^{{x}} }{\mathrm{4}^{{x}} +\mathrm{9}^{{x}} }{dx}=? \\ $$ Answered by qaz last updated on 11/Nov/21 $$\int\frac{\mathrm{6}^{\mathrm{x}} }{\mathrm{4}^{\mathrm{x}} +\mathrm{9}^{\mathrm{x}}…
Question Number 93473 by mashallah last updated on 13/May/20 $$\int\mathrm{1}/\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} \\ $$ Commented by abdomathmax last updated on 15/May/20 $${A}\:=\int\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:\:{we}\:{do}\:{the}\:{changement}\:{x}\:={tant}\:\Rightarrow \\ $$$${A}\:\:=\int\:\:\:\frac{\left(\mathrm{1}+{tan}^{\mathrm{2}}…
Question Number 93471 by mashallah last updated on 13/May/20 $$\int\mathrm{1}/\mathrm{1}+\mathrm{x2} \\ $$ Answered by Rio Michael last updated on 13/May/20 $$\int\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\:{dx}\:=\:\mathrm{arctan}\:{x}\:+\:{C} \\ $$ Terms…