Question Number 151549 by mathdanisur last updated on 21/Aug/21 $$\mathrm{Compare}: \\ $$$$\mathrm{2}^{\mathrm{2}^{\mathrm{2}^{.^{.^{.} } } } } \:\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{3}^{\mathrm{3}^{\mathrm{3}^{.^{.^{.} } } } } \\ $$$$\mathrm{Here}\:\mathrm{it}\:\mathrm{is}\:\mathrm{raised}\:\mathrm{1001}\:\mathrm{times}\:\mathrm{a}\:\mathrm{square}, \\ $$$$\mathrm{1000}\:\mathrm{times}\:\mathrm{a}\:\mathrm{cube}.…
Question Number 86015 by mathmax by abdo last updated on 26/Mar/20 $${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{2}\right)^{\mathrm{4}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 86013 by mathmax by abdo last updated on 26/Mar/20 $${calculate}\:\:\int_{\mathrm{1}+\sqrt{\mathrm{2}}} ^{+\infty} \:\:\:\:\frac{{dx}}{\left({x}−\mathrm{1}\right)^{\mathrm{3}} \left({x}+\mathrm{2}\right)^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 86008 by TawaTawa1 last updated on 26/Mar/20 Commented by jagoll last updated on 26/Mar/20 $$\mathrm{10}^{\mathrm{o}} \\ $$ Commented by TawaTawa1 last updated on…
Question Number 86009 by M±th+et£s last updated on 26/Mar/20 $${solve}\:{in}\:{R}\::\left[\frac{{x}}{\mathrm{2}}\right]+\left[\frac{\mathrm{2}{x}}{\mathrm{3}}\right]−{x}=\mathrm{0} \\ $$ Answered by MJS last updated on 26/Mar/20 $$\left[\frac{{x}}{\mathrm{2}}\right]\in\mathbb{Z}\wedge\left[\frac{\mathrm{2}{x}}{\mathrm{3}}\right]\in\mathbb{Z}\Rightarrow{x}\in\mathbb{Z} \\ $$$$\mathrm{let}\:{k},\:{m},\:{n}\:\in\mathbb{Z} \\ $$$$\left[\frac{{x}}{\mathrm{2}}\right]=\begin{cases}{\frac{{x}}{\mathrm{2}};\:{x}=\mathrm{2}{m}}\\{\frac{{x}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}};\:{x}=\mathrm{2}{m}+\mathrm{1}}\end{cases} \\…
Question Number 20471 by ajfour last updated on 27/Aug/17 $${Find}\:{the}\:{surface}\:{area}\:{of}\:{a}\:{solid} \\ $$$${that}\:{is}\:{common}\:{part}\:{of}\:{two} \\ $$$${cylinders}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={a}^{\mathrm{2}} ,\:{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={a}^{\mathrm{2}} . \\ $$$$\boldsymbol{{Compute}}\:\boldsymbol{{the}}\:\boldsymbol{{volume}}\:\boldsymbol{{also}}. \\ $$ Commented…
Question Number 20468 by tammi last updated on 27/Aug/17 $$\int\frac{{dx}}{\mathrm{sin}\:^{\mathrm{4}} {x}−\mathrm{cos}\:^{\mathrm{4}} {x}} \\ $$ Answered by ajfour last updated on 27/Aug/17 $$−\int\mathrm{sec}\:\mathrm{2}{xdx}=−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{sec}\:\mathrm{2}{x}+\mathrm{tan}\:\mathrm{2}{x}\mid+{C}\:. \\ $$ Terms…
Question Number 20467 by tammi last updated on 27/Aug/17 $$\int\left({a}\mathrm{sin}\:^{\mathrm{2}} {x}+{b}\mathrm{cos}\:^{\mathrm{2}} {x}\right){dx} \\ $$ Answered by ajfour last updated on 27/Aug/17 $$=\frac{{a}}{\mathrm{2}}\int\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}\right){dx}+\frac{{b}}{\mathrm{2}}\int\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}\right){dx} \\ $$$$=\frac{{a}}{\mathrm{2}}\left({x}−\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{2}}\right)+\frac{{b}}{\mathrm{2}}\left({x}+\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{2}}\right)+{C} \\…
Question Number 86003 by jagoll last updated on 26/Mar/20 $$\mathrm{y}\:''\:+\:\mathrm{y}'\:=\:\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x} \\ $$ Commented by mathmax by abdo last updated on 26/Mar/20 $${let}\:{y}^{'} ={z}\:\:\:\left({e}\right)\Rightarrow{z}^{'} \:+{z}\:={sinx}\:{cos}\mathrm{2}{x} \\…
Question Number 20466 by tammi last updated on 27/Aug/17 $$\int\frac{\mathrm{sin}\:{x}\mathrm{cos}\:{xdx}}{\mathrm{sin}^{\mathrm{4}} {x}+\mathrm{cos}\:^{\mathrm{4}} {x}} \\ $$ Answered by sma3l2996 last updated on 27/Aug/17 $${t}={sin}^{\mathrm{2}} {x}\Rightarrow{dt}=\mathrm{2}{sinxcosxdx} \\ $$$${I}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dt}}{{t}^{\mathrm{2}}…