Question Number 138733 by mnjuly1970 last updated on 17/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{mathematical}\:….{analysis}….. \\ $$$$\:\:{suppose}\:\:\:\:{f}\::\left[{a}\:,\:{b}\right]\rightarrow\mathbb{R}\:{is}\:{a}\:{function} \\ $$$$\:\:\:{and}\:\:\:\alpha:\left[{a}\:,\:{b}\right]\overset{\alpha\nearrow} {\rightarrow}\mathbb{R}\:\left(\alpha\:{is}\:{an}\:{increasing}\:{function}\right. \\ $$$$\left.\:{on}\:\left[{a}\:,\:{b}\right]\right)\:\:{meanwhile}\:\alpha\:{is}\:{continuous}\:{at}\:{y}_{\mathrm{0}} \: \\ $$$$\:\:{where}\:\:\:{a}\leqslant{y}_{\mathrm{0}} \leqslant{b}\:\:.\:{defining}\: \\ $$$$\:\:\:{f}\left({x}\right)=\begin{cases}{\:\mathrm{1}\:\:\:\:\:\:\:\:\:{x}={y}_{\mathrm{0}} }\\{\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:{x}\neq{y}_{\mathrm{0}} }\end{cases}…
Question Number 138728 by qaz last updated on 17/Apr/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{ln}\left(\mathrm{1}+\mathrm{cos}\:{x}\right)}{\mathrm{1}+{e}^{{x}} }{dx}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73182 by mathmax by abdo last updated on 07/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{xe}^{−{x}^{\mathrm{2}} } {arctan}\left({x}−\frac{\mathrm{1}}{{x}}\right){dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 138723 by mnjuly1970 last updated on 17/Apr/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:……..{advanced}…\:…\:…{math}…… \\ $$$$\:{prove}\:{that}\:_{\ast} ^{\ast} \:\::::: \\ $$$$\:\:\:\boldsymbol{\Omega}=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\left\{\frac{\mathrm{1}}{\mathrm{16}^{{k}} }\left(\frac{\mathrm{4}}{\mathrm{8}{k}+\mathrm{1}}−\frac{\mathrm{2}}{\mathrm{8}{k}+\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{8}{k}+\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{8}{k}+\mathrm{6}}\right)\right\}=\pi \\ $$$$\:\:\:\:\:\:\:\:\:….{Bailey}−{Borwein}\:{formula}…. \\ $$$$\:\:\:…
Question Number 73180 by mathmax by abdo last updated on 07/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73179 by mathmax by abdo last updated on 07/Nov/19 $${caoculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} −\mathrm{1}\right)}{\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 73178 by mathmax by abdo last updated on 07/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx} \\ $$ Answered by mind is power last updated…
Question Number 73181 by mathmax by abdo last updated on 07/Nov/19 $${calculate}\:\int_{\mathrm{1}} ^{\mathrm{3}\:} \:\frac{{x}−\mathrm{2}}{\:\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 7637 by Tawakalitu. last updated on 07/Sep/16 $$\int{x}^{{x}} \:{dx} \\ $$ Answered by FilupSmith last updated on 07/Sep/16 $${x}^{{x}} ={e}^{{x}\mathrm{ln}\left({x}\right)} =\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{n}}…
Question Number 138710 by bramlexs22 last updated on 17/Apr/21 $$\underset{\mathrm{1}} {\int}^{\:\infty} \:\frac{\mathrm{ln}\:{x}}{\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\:{dx}\:=? \\ $$ Answered by mathmax by abdo last updated on 17/Apr/21 $$\Phi=\int_{\mathrm{1}}…