Question Number 5498 by Yozzii last updated on 16/May/16 $$\left(\mathrm{1}+{abc}\right)^{\mathrm{3}} \geqslant{abc}\left(\mathrm{1}+{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{c}\right)\: \\ $$$${if}\:{a},{b},{c}>\mathrm{0}? \\ $$ Answered by Rasheed Soomro last updated on 17/May/16 Commented by…
Question Number 136570 by mnjuly1970 last updated on 23/Mar/21 $$\:\:\:\:\:\:\:\:\:…….{nice}\:\:…..\:\:\:{calculus}….. \\ $$$$\:\:\:\:\Omega=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{cos}^{{n}} \left({x}\right).{cos}\left({nx}\right)=? \\ $$$$\:\:\:{solution}:::: \\ $$$$\:\:\:\:\Omega=\frac{\mathrm{1}}{\mathrm{2}}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{cos}^{{n}−\mathrm{1}} \left({x}\right)\left\{{cos}\left({x}−{nx}\right)+{cos}\left({x}+{nx}\right)\right. \\ $$$$\:\:\therefore\:\mathrm{2}\Omega=\underset{{n}=\mathrm{0}} {\overset{\infty}…
Question Number 5495 by FilupSmith last updated on 16/May/16 $$\mathrm{Why}\:\mathrm{does}: \\ $$$$\mathrm{cos}^{\mathrm{2}} {x}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{cos}\left(\mathrm{2}{x}\right)+\mathrm{1}\right) \\ $$ Commented by Yozzii last updated on 16/May/16 $${Let}\:\boldsymbol{{a}}=\begin{pmatrix}{{cosA}}\\{{sinA}}\end{pmatrix}\:,\boldsymbol{{b}}=\begin{pmatrix}{{cosB}}\\{−{sinB}}\end{pmatrix}. \\ $$$${For}\:{all}\:\mathrm{0}<{A},{B}<\mathrm{2}\pi,\:{the}\:{angle}\:{between}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}\:{is}\:{A}+{B}…
Question Number 5490 by 123456 last updated on 16/May/16 $$\int\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=? \\ $$$$\underset{−{r}} {\overset{{x}} {\int}}\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=?? \\ $$$$\underset{{x}} {\overset{{y}} {\int}}\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=??? \\…
Question Number 5487 by love math last updated on 16/May/16 $$\int{sin}\:{x}\:{ln}\:\left({tan}\:{x}\right)\:{dx} \\ $$$$ \\ $$$$\int{x}^{{n}} {ln}\:{x}\:{dx}\:\:\:\:\:\:\:\:\:\left({n}\neq−\mathrm{1}\right) \\ $$$$ \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{2}}}{dx} \\ $$$$ \\…
Question Number 5486 by love math last updated on 16/May/16 $$\int{sin}\:{x}\:{ln}\:\left({tan}\:{x}\right)\:{dx} \\ $$$$ \\ $$$$\int{x}^{{n}} {ln}\:{x}\:{dx}\:\:\:\:\:\:\:\:\:\left({n}\neq−\mathrm{1}\right) \\ $$$$ \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{2}}}{dx} \\ $$$$ \\…
Question Number 136559 by mohammad17 last updated on 23/Mar/21 $${show}\:{that}\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{{n}−\mathrm{4}}{{n}^{\mathrm{2}} −\mathrm{2}{n}+\mathrm{1}}\:{is}\:{converge}\:{or}\:{diverge}\: \\ $$$$ \\ $$$${by}\:{ussing}\:{any}\:{test} \\ $$ Commented by mr W last updated…
Question Number 136555 by mnjuly1970 last updated on 23/Mar/21 $$\:\:\:\:\:\:\:\:\:….{nice}\:\:\:\:……\:\:\:{calculus}…. \\ $$$$\:\:\:{prove}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{2}}{ln}\left(\mathrm{2}\right)−\frac{\pi}{\mathrm{4}} \\ $$$$\:\:\:\:\::::::::: \\ $$ Answered by…
Question Number 71016 by mr W last updated on 10/Oct/19 $$\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+…\right)\right)\right)=? \\ $$ Answered by mr W last updated on 11/Oct/19 $$\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+…\right)\right)\right)={x} \\ $$$$\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+{x}\right)={x} \\…
Question Number 71014 by mathmax by abdo last updated on 10/Oct/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left({x}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)} {dx} \\ $$ Terms of Service Privacy Policy Contact:…