Question Number 128279 by liberty last updated on 06/Jan/21 $$\:\:\Theta\:=\:\int_{\mathrm{1}} ^{\:\mathrm{e}} \:\frac{{dx}}{{x}.\sqrt[{\mathrm{3}}]{\mathrm{ln}\:{x}}}\:?\: \\ $$ Answered by john_santu last updated on 06/Jan/21 $$\:{let}\:\sqrt[{\mathrm{3}\:}]{\mathrm{ln}\:{x}}\:=\:{w}\:\Rightarrow\:\frac{{dx}}{{x}}\:=\:\mathrm{3}{w}^{\mathrm{2}} \:{dw} \\ $$$$\:\Theta\:=\:\int_{\mathrm{0}}…
Question Number 128225 by mnjuly1970 last updated on 05/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\phi\:=\:\int_{\mathrm{0}} ^{\:\pi} \frac{{tan}^{−\mathrm{1}} \left({tan}^{\mathrm{2}} \left({x}\right)\right)}{{tan}^{\mathrm{2}} \left({x}\right.}\:{dx}\overset{???} {=}\pi\left(\sqrt{\mathrm{2}}\:−\frac{\pi}{\mathrm{4}}\right) \\ $$$$ \\ $$ Answered…
Question Number 62679 by ajfour last updated on 24/Jun/19 $${Let}\:{f}\:{be}\:{defined}\:{in}\:{the}\:{neighborhood} \\ $$$${of}\:{x}\:{and}\:{that}\:{f}\:''\left({x}\right)\:{exists}. \\ $$$${Prove}\:{that}\:\: \\ $$$$\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left({x}+{h}\right)+{f}\left({x}−{h}\right)−\mathrm{2}{f}\left({x}\right)}{{h}^{\mathrm{2}} }={f}\:''\left({x}\right)\:. \\ $$ Commented by kaivan.ahmadi last updated…
Question Number 128156 by DomaPeti last updated on 04/Jan/21 $${f}\left({x}\right)''=\frac{\mathrm{1}}{{f}\left({x}\right)^{\mathrm{2}} }\:\:\:\:\: \\ $$$${f}\left({x}\right)=? \\ $$ Answered by mr W last updated on 05/Jan/21 $${let}\:{y}'={u} \\…
Question Number 128105 by snipers237 last updated on 04/Jan/21 $${Let}\:{f}\:\:\:\mathbb{N}^{\ast} \rightarrow\mathbb{N}^{\ast} \:{a}\:{bijection}\: \\ $$$${Prove}\:{that}\:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{f}\left({k}\right)\geqslant\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128005 by mnjuly1970 last updated on 03/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:\:{calculus}… \\ $$$$\:\:{if}\:\:{b}>{a}>\mathrm{0}\:{then}\:{prove}\::: \\ $$$$\:\:\:\:\:\:\:\:\frac{{a}+{b}}{\mathrm{2}}>\:\frac{{b}−{a}}{{ln}\left({b}\right)−{ln}\left({a}\right)}\:>\:\sqrt{{ab}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………………………. \\ $$ Answered by mindispower last updated on 06/Jan/21…
Question Number 62438 by mathsolverby Abdo last updated on 21/Jun/19 $${splve}\:{x}^{\mathrm{2}} {y}^{''} \:−\left({x}+\mathrm{1}\right){y}'\:\:\:=\left({x}+\mathrm{1}\right){e}^{−{x}} \\ $$$$ \\ $$$$ \\ $$ Commented by mathmax by abdo last…
Question Number 127929 by mnjuly1970 last updated on 03/Jan/21 $$ \\ $$$$\:\:\:\:\:\:\phi=\int_{\mathrm{1}} ^{\:\infty} \frac{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}}{{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx}=? \\ $$ Answered by Ar Brandon last updated…
Question Number 127839 by mnjuly1970 last updated on 02/Jan/21 $$\:\:\: \\ $$$${if}\:\:\Omega\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}−{x}\right)\Gamma\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)}{\Gamma\left(\mathrm{2}−\frac{{x}}{\mathrm{2}}\right)\left(\frac{{x}}{\mathrm{2}}−\mathrm{1}\right)}\right){dx} \\ $$$$\:\:{find}\:\:\:\:\frac{{Re}\left(\Omega\right)}{{Im}\left(\Omega\right)}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62291 by rajesh4661kumar@gamil.com last updated on 19/Jun/19 Commented by maxmathsup by imad last updated on 19/Jun/19 $$\Rightarrow\left({e}^{{x}} −\mathrm{1}\right){e}^{{y}} \:={e}^{{x}} \:\Rightarrow{e}^{{y}} \:=\frac{{e}^{{x}} }{{e}^{{x}} −\mathrm{1}}\:\Rightarrow{y}\:={ln}\left(\frac{{e}^{{x}}…