Question Number 153040 by mnjuly1970 last updated on 04/Sep/21 $$ \\ $$$$\:{prove}\:{that}.. \\ $$$$ \\ $$$$\Omega\:=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}\:\left({x}\:\right)}{{sinh}\left({x}\right)}{dx}\:=\frac{\pi}{\mathrm{2}}\:{tanh}\:\left(\frac{\pi}{\mathrm{2}}\right)\:\: \\ $$ Terms of Service Privacy Policy…
Question Number 87503 by M±th+et£s last updated on 04/Apr/20 $$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{5}} }{dx} \\ $$ Commented by MJS last updated on 04/Apr/20 $${x}^{\mathrm{5}} +\mathrm{1}=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}+\mathrm{1}\right)…
Question Number 21965 by j.masanja06@gmail.com last updated on 07/Oct/17 $${integrate} \\ $$$$\int{sin}^{\mathrm{3}} {xdx} \\ $$ Answered by Tikufly last updated on 07/Oct/17 $$\:\:=\int\:\left(\mathrm{sin}^{\mathrm{2}} {x}\right)\mathrm{sin}{xdx} \\…
Question Number 87461 by hamdhan last updated on 04/Apr/20 $$\underset{{e}^{-\mathrm{1}} } {\overset{\mathrm{e}} {\int}}\:\frac{\sqrt{\mathrm{1}−\left(\mathrm{ln}{x}\right)^{\mathrm{2}} }}{{x}}\:{dx} \\ $$ Commented by ajfour last updated on 04/Apr/20 $${let}\:\:\mathrm{ln}\:{x}={t}\:\:\:\:\Rightarrow\:\:\left({dx}\right)/{x}={dt} \\…
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}?…