Question Number 87527 by mathmax by abdo last updated on 04/Apr/20 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{3}{x}\right)}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 153063 by talminator2856791 last updated on 04/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\: \\ $$$$\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:\:{dx} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{is}\:\mathrm{unsolvable} \\ $$$$\:…
Question Number 87511 by M±th+et£s last updated on 04/Apr/20 Answered by TANMAY PANACEA. last updated on 04/Apr/20 $${t}={x}^{\mathrm{3}} \rightarrow\frac{{dt}}{\mathrm{3}}={x}^{\mathrm{2}} {dx} \\ $$$$\int_{{ln}\mathrm{3}} ^{{ln}\mathrm{4}} \frac{\mathrm{1}}{\mathrm{3}}×\frac{{sint}}{{sint}+{sin}\left({ln}\mathrm{12}−{t}\right)}{dt}\:={I} \\…
Question Number 21970 by j.masanja06@gmail.com last updated on 07/Oct/17 $${integrate} \\ $$$$\int{sec}^{\mathrm{3}} {xdx} \\ $$ Answered by Tikufly last updated on 07/Oct/17 $$\:\int\mathrm{sec}^{\mathrm{3}} {xdx}=\int\:\left(\mathrm{sec}{x}\right)\left(\mathrm{sec}^{\mathrm{2}} {x}\right){dx}…
Question Number 153040 by mnjuly1970 last updated on 04/Sep/21 $$ \\ $$$$\:{prove}\:{that}.. \\ $$$$ \\ $$$$\Omega\:=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}\:\left({x}\:\right)}{{sinh}\left({x}\right)}{dx}\:=\frac{\pi}{\mathrm{2}}\:{tanh}\:\left(\frac{\pi}{\mathrm{2}}\right)\:\: \\ $$ 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…