Question Number 166180 by mnjuly1970 last updated on 15/Feb/22 $$ \\ $$$$\:\:\:\:\:\:{prove}\:\:{that} \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}\:\right)}{{x}^{\:\mathrm{2}} }\:{dx}\:=\:\mathrm{2}\:\zeta\:\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:−−−{proof}−−− \\ $$$$\:\:\:\:\boldsymbol{\phi}=\:\left[\frac{−\mathrm{1}}{{x}}\:{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}\right)\:\right]_{\mathrm{0}} ^{\mathrm{1}} −\int_{\mathrm{0}}…
Question Number 35101 by ajfour last updated on 15/May/18 $${Find}\:{volume}\:{enclosed}\:{by} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{{c}^{\mathrm{2}} }=\mathrm{1}\:\:. \\ $$ Commented by behi83417@gmail.com last updated…
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Question Number 35062 by math khazana by abdo last updated on 14/May/18 $${calculate}\:{A}_{{n}} \:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{4}} \:+\mathrm{1}\right)^{{n}} } \\ $$$${with}\:{n}\:{integr}\:{natural}\:. \\ $$ Terms of Service…
Question Number 35061 by math khazana by abdo last updated on 14/May/18 $${find}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{x}^{\mathrm{2}} \:+\mathrm{3}}{\left({x}^{\mathrm{4}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by math khazana by…
Question Number 35060 by math khazana by abdo last updated on 14/May/18 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sinx}\:{ln}\left({cosx}\right){dx} \\ $$ Commented by math khazana by abdo last updated…
Question Number 35058 by math khazana by abdo last updated on 14/May/18 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{cos}^{\mathrm{2}} {t}\right)^{\mathrm{3}} } \\ $$ Commented by abdo mathsup 649 cc…
Question Number 35059 by math khazana by abdo last updated on 14/May/18 $${find}\:\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\:\frac{{dx}}{{cosx}\:+{sinx}} \\ $$ Commented by math khazana by abdo last updated…
Question Number 100590 by Rohit@Thakur last updated on 27/Jun/20 $$\int_{\mathrm{0}} ^{\infty} \:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{18}} \right)^{\mathrm{2}} } \\ $$ Answered by mathmax by abdo last updated on 27/Jun/20…