Question Number 95547 by Fikret last updated on 25/May/20 $$\int\frac{\mathrm{2}{x}^{\mathrm{3}} {dx}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}=? \\ $$ Answered by MJS last updated on 25/May/20 $$\int\frac{\mathrm{2}{x}^{\mathrm{3}} }{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}{dx}=\int\left({x}+\mathrm{2}+\frac{\mathrm{5}{x}−\mathrm{6}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}\right){dx}=…
Question Number 95546 by Fikret last updated on 25/May/20 $$\int{x}^{\mathrm{2}} \sqrt{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }{dx}=? \\ $$ Answered by MJS last updated on 25/May/20 $$\int{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} +{a}^{\mathrm{2}}…
Question Number 161076 by mnjuly1970 last updated on 11/Dec/21 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\:\left(\mathrm{1}+\:{x}\:\right)}{\left(\mathrm{1}+\:{x}^{\:\mathrm{2}} \right)^{\:\mathrm{2}} }\:{dx}\:=\:? \\ $$$$\:\:\:\:\:−−−−−−−−−−−− \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered…
Question Number 30008 by Jmasanja last updated on 14/Feb/18 $${integrate}\:{w}.{r}.{t}\:{x} \\ $$$$\int\left({e}^{{x}^{\mathrm{2}} } \right){dx} \\ $$ Commented by abdo imad last updated on 14/Feb/18 $${we}\:{have}\:{e}^{{u}}…
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Question Number 29980 by abdo imad last updated on 14/Feb/18 $${prove}\:{that}\:\gamma=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(\frac{\mathrm{1}}{{n}}\:\:−{ln}\left(\mathrm{1}\:+\frac{\mathrm{1}}{{n}}\right)\right) \\ $$$$\left.\mathrm{2}\right){show}\:{that}\:\gamma=\:\sum_{{k}=\mathrm{2}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\xi\left({k}\right). \\ $$ Terms of Service Privacy Policy…
Question Number 29975 by abdo imad last updated on 14/Feb/18 $$\:{let}\:{give}\:\mathrm{0}<\alpha<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\pi\:{coth}\left(\pi\alpha\right)\:−\frac{\mathrm{1}}{\alpha}\:=\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\mathrm{2}\alpha}{\alpha^{\mathrm{2}} \:+{n}^{\mathrm{2}} }. \\ $$$$\left.\mathrm{2}\right){by}\:{integration}\:{on}\left[\mathrm{0},\mathrm{1}\right]\:{find}\:\prod_{{n}=\mathrm{1}} ^{\infty} \:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right). \\ $$ Commented…
Question Number 29976 by abdo imad last updated on 14/Feb/18 $${prove}\:{that} \\ $$$${ln}\left(\Gamma\left({x}\right)\right)=\:−{lnx}\:−\gamma{x}\:\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(\:\:\frac{{x}}{{n}}\:\:−{ln}\left(\:\mathrm{1}+\frac{{x}}{{n}}\right)\right)\:{with}\:{x}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 29971 by abdo imad last updated on 14/Feb/18 $${find}\:{J}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{{x}+{e}^{{t}} }\:\:\:\:?. \\ $$ Commented by abdo imad last updated on 16/Feb/18 $${J}\left({x}\right)=\:\int_{\mathrm{0}}…
Question Number 29972 by abdo imad last updated on 14/Feb/18 $${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:{find}\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{d}\theta}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} {cos}^{\mathrm{2}} \theta}}\:. \\ $$ Commented by abdo imad last updated on 18/Feb/18…