Question Number 132733 by bagjagunawan last updated on 16/Feb/21 $$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{log}\:{x}}{\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} }\:{dx}=…? \\ $$ Answered by Ajetunmobi last updated on 16/Feb/21 Terms of…
Question Number 132729 by mnjuly1970 last updated on 16/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{advanced}\:\:\:{calculus}… \\ $$$$\:\:\:\:{evaluate}\:: \\ $$$$\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} {xe}^{−\mathrm{2}{x}} {ln}\left({x}\right){dx}=??? \\ $$$$ \\ $$ Answered by Olaf last…
Question Number 67197 by necxxx last updated on 23/Aug/19 $$\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{\mathrm{5}} \left(\mathrm{1}−\frac{{x}}{\mathrm{2}}\right)^{\mathrm{4}} {dx} \\ $$ Answered by turbo msup by abdo last updated on…
Question Number 1643 by 112358 last updated on 28/Aug/15 $${Calculate}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}\left({a},{b}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {t}^{{a}} \left(\mathrm{1}−{t}\right)^{{b}} {dt} \\ $$$${given}\:{that}\:{I}\left({a},{b}\right)=\frac{{b}}{{a}+\mathrm{1}}{I}\left({a}+\mathrm{1},{b}−\mathrm{1}\right) \\ $$$$\left({a}>\mathrm{0},{b}>\mathrm{0}\right).\:{Use}\:{the}\:{fact}\:{that} \\ $$$${I}\left({a},{b}\right)={I}\left({a}+\mathrm{1},{b}\right)+{I}\left({a},{b}+\mathrm{1}\right) \\ $$$${and}\:{I}\left({a},{b}\right)={I}\left({b},{a}\right)\: \\…
Question Number 132708 by frc2crc last updated on 16/Feb/21 $$\int_{−\infty} ^{\infty} \frac{{x}^{\mathrm{2}} \mathrm{cos}\:\left({px}+{q}\right)}{{x}^{\mathrm{2}} +\left({p}+{q}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by Olaf last updated on 16/Feb/21 $$…
Question Number 1625 by 112358 last updated on 27/Aug/15 $${y}\left({x}\right)=\frac{\mathrm{1}}{{x}−{a}}\int_{{a}} ^{{x}} \sqrt{{t}+\sqrt{{t}+\sqrt{{t}+\sqrt{{t}+\sqrt{{t}+…}}}}}{dt} \\ $$$${x}\neq{a},\:{a}>\mathrm{0},{y}\left({x}\right)>\mathrm{0}. \\ $$$${Find}\:\:{y}\left(\mathrm{2}{a}\right). \\ $$ Answered by Rasheed Soomro last updated on…
Question Number 132693 by liberty last updated on 15/Feb/21 $$\mathrm{I}=\int\:\frac{{dx}}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }\: \\ $$ Answered by EDWIN88 last updated on 15/Feb/21 $$\mathrm{Ostrogradsky}\:\mathrm{again} \\ $$$$\int\:\frac{{dx}}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}}…
Question Number 67153 by mhmd last updated on 23/Aug/19 $${find}\:\int\left({v}^{\mathrm{3}} −\mathrm{2}\right)/\left({v}^{\mathrm{4}} +{v}\:\:\right){dv} \\ $$ Answered by mhmd last updated on 23/Aug/19 $$ \\ $$ Answered…
Question Number 1613 by 112358 last updated on 26/Aug/15 $$\mathrm{Compute}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}−\mathrm{1}}{{logx}}{dx}\:. \\ $$ Commented by 123456 last updated on 27/Aug/15 $$\mathrm{I}=\mathrm{ln}\:\mathrm{10}\:\mathrm{ln}\:\mathrm{2} \\…
Question Number 67138 by mhmd last updated on 23/Aug/19 $${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${and}\:{y}={x}−\mathrm{2}? \\ $$ Commented by mr W last updated on 23/Aug/19 $${sir}:\:{you}\:{don}'{t}\:{need}\:{to}\:{repeat}\:{the} \\ $$$${same}\:{question}\:{so}\:{frequently}.…