Question Number 21904 by ajfour last updated on 06/Oct/17 $${Compute}\:{the}\:{area}\:{of}\:{a}\:{loop}\:{of}\:{the} \\ $$$${curve}\:\left(\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\right)=\frac{\mathrm{2}{xy}}{{c}^{\mathrm{2}} }\:. \\ $$ Commented by math solver last updated…
Question Number 152939 by mnjuly1970 last updated on 03/Sep/21 $$ \\ $$$$\:\:\:\:\:\mathrm{Q}\::\:\:\mathrm{If}\:\:\:\:{a}\:\:,\:\:{b}\:\:\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers}\:\:\mathrm{and} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\:\:{a}\:=\:\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\:\mathrm{6}{a}\:−\mathrm{2}}\:\:}\\{\:\:\:{b}\:=\:\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\:\mathrm{6}{b}\:−\mathrm{2}}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:,\:\:\:\:{a}.{b}\:=? \\ $$$$\:\:\:\:…\:\mathrm{Compiled}\:\mathrm{by}\:\mathrm{m}.\mathrm{n}\::\:\left(\mathscr{E}\:{lementary}\:{olympiad}\:\right).\:\:\:\:\:\:\blacksquare \\ $$$$ \\ $$ Answered…
Question Number 152910 by 281981 last updated on 03/Sep/21 $$\int^{} {x}^{{x}^{{x}} } {dx}= \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 87371 by M±th+et£s last updated on 04/Apr/20 $$\int\frac{{x}^{\mathrm{7}} +{x}^{\mathrm{3}} +\mathrm{4}}{{x}^{\mathrm{8}} −{x}^{\mathrm{5}} +\mathrm{9}}{dx} \\ $$ Commented by M±th+et£s last updated on 04/Apr/20 $${why}\:{sir} \\…
Question Number 21810 by j.masanja06@gmail.com last updated on 04/Oct/17 $${integrate} \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by sma3l2996 last updated on 04/Oct/17 $${x}={sint}\Rightarrow{dx}={costdt}=\sqrt{\mathrm{1}−{sin}^{\mathrm{2}} {t}}{dt}…
Question Number 87340 by john santu last updated on 04/Apr/20 $$\int\:\frac{\mathrm{cos}\:\mathrm{x}}{\left(\mathrm{5}+\mathrm{4cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}\:= \\ $$ Commented by john santu last updated on 04/Apr/20 $$\mathrm{dear}\:\mathrm{mr}\:\mathrm{Mjs}.\:\mathrm{whether}\:\mathrm{methods}\: \\ $$$$\mathrm{besides}\:\mathrm{weierstrass}\:\mathrm{substitution}?…
Question Number 152874 by mnjuly1970 last updated on 02/Sep/21 $$ \\ $$$$\:\:\:{solve}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\:{tanh}\:\left({x}\right)\:}{{x}}\:\right)^{\:\mathrm{2}} {dx}\:=\:? \\ $$$$\:\:{m}.{n}. \\ $$ Answered by Ar Brandon…
Question Number 152861 by talminator2856791 last updated on 02/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\int_{−\infty} ^{\:\infty} \frac{\left(\mathrm{ln}\left(\left({x}^{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}} +\mathrm{1}\right)^{\mathrm{2}} +\mathrm{1}\right)\right)^{−\mathrm{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)} }{\:\sqrt{{x}^{\mid\lfloor{x}\rfloor\mid} +\mathrm{1}}}\:\:{dx} \\ $$$$\: \\…
Question Number 152866 by talminator2856791 last updated on 02/Sep/21 $$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{ln}\left(\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}\right)}{\left(\mathrm{ln}\left(\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{3}} \right)\right)^{\mathrm{2}} }\:\:{dx} \\ $$$$\: \\ $$$$\: \\…
Question Number 87325 by M±th+et£s last updated on 04/Apr/20 $$\left.\mathrm{1}\right)\:\int{e}^{\sqrt{{x}}} \:{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{\sqrt{{sin}\left({x}\right)}}{\:\sqrt{{sin}\left({x}\right)}+\sqrt{{cos}\left({x}\right)}}{dx} \\ $$ Commented by Serlea last updated on 04/Apr/20 $$\left.\mathrm{1}\right)\:\int\mathrm{e}^{\sqrt{\mathrm{x}}} \mathrm{dx} \\…