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 $$\Phi=\int_{\mathrm{1}}…
Question Number 73155 by MJS last updated on 06/Nov/19 $$\mathrm{reposting}\:\mathrm{a}\:\mathrm{former}\:\mathrm{question}… \\ $$$$\int\frac{\sqrt[{\mathrm{5}}]{{x}}−\mathrm{1}}{\:\sqrt{{x}}+\mathrm{1}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt[{\mathrm{10}}]{{x}}\:\rightarrow\:{dx}=\mathrm{10}\sqrt[{\mathrm{10}}]{{x}^{\mathrm{9}} }{dx}\right] \\ $$$$=\mathrm{10}\int\frac{{t}^{\mathrm{9}} \left({t}−\mathrm{1}\right)}{{t}^{\mathrm{4}} −{t}^{\mathrm{3}} +{t}^{\mathrm{2}} −{t}+\mathrm{1}}{dt}= \\ $$$$=\mathrm{10}\int\left({t}^{\mathrm{6}} −{t}^{\mathrm{4}} −{t}\right){dt}+\mathrm{10}\int\frac{{t}\left({t}^{\mathrm{2}}…
Question Number 138691 by liberty last updated on 16/Apr/21 $$\int\:\mathrm{cos}\:\mathrm{2}{x}\:\sqrt{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} {x}}\:{dx}\:=? \\ $$ Answered by mathmax by abdo last updated on 17/Apr/21 $$\mathrm{I}=\int\:\mathrm{cos}\left(\mathrm{2x}\right)\sqrt{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}\:\Rightarrow\mathrm{I}=\int\:\mathrm{cos}\left(\mathrm{2x}\right)\sqrt{\mathrm{1}+\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{2}}}\mathrm{dx} \\…
Question Number 73147 by amaramariche last updated on 06/Nov/19 $$\int\frac{{x}−\mathrm{6}}{{x}^{\mathrm{3}} +\mathrm{1}}{dx} \\ $$$$ \\ $$ Commented by mathmax by abdo last updated on 07/Nov/19 $${let}\:{A}\:=\int\:\frac{{x}−\mathrm{6}}{{x}^{\mathrm{3}}…