Question Number 35139 by behi83417@gmail.com last updated on 15/May/18 Commented by abdo mathsup 649 cc last updated on 16/May/18 $${let}\:{put}\:{I}\:=\:\int_{\mathrm{0}} ^{\sqrt{\mathrm{2}}} \:\:\:\:\frac{{x}+\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}}{dx} \\ $$$${I}\:=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}}…
Question Number 166192 by greogoury55 last updated on 15/Feb/22 $$\:\:\:\:\int\:\frac{{dx}}{\mathrm{5}+\mathrm{4sin}\:{x}}\:=? \\ $$ Answered by som(math1967) last updated on 15/Feb/22 $$\:\:\int\frac{{dx}}{\mathrm{5}\left({sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}+{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}\right)+\mathrm{8}{sin}\frac{{x}}{\mathrm{2}}{cos}\frac{{x}}{\mathrm{2}}} \\ $$$$=\int\frac{{sec}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}{dx}}{\mathrm{5}{tan}^{\mathrm{2}}…
Question Number 166191 by cortano1 last updated on 15/Feb/22 $$\:\:\:\:\:\:\:\underset{−\frac{\pi}{\mathrm{2}}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{dx}=? \\ $$ Answered by phanphuoc last updated on 15/Feb/22 $${f}\:{odd}\:\rightarrow{i}=\mathrm{0} \\…
Question Number 100657 by Cheyboy last updated on 28/Jun/20 $$\int\:\:\frac{\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{9}}\:{dx} \\ $$ Commented by bobhans last updated on 28/Jun/20 $$\mathrm{set}\:\mathrm{x}\:=\:\mathrm{3tan}\:\mathrm{z}\:\Rightarrow\:\mathrm{dx}\:=\:\mathrm{3sec}\:^{\mathrm{2}} \mathrm{dz} \\ $$$$\mathrm{I}=\int\:\frac{\mathrm{2x}+\mathrm{x}−\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{9}}\:\mathrm{dx}\:=\int\:\frac{\mathrm{d}\left(\mathrm{x}^{\mathrm{2}}…
Question Number 100653 by Ar Brandon last updated on 28/Jun/20 Answered by mathmax by abdo last updated on 28/Jun/20 $$\left.\mathrm{1}\left.\right)\left.\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{sin}\left(\mathrm{nx}\right)}{\mathrm{sinx}}\:\mathrm{is}\:\mathrm{continue}\:\:\mathrm{on}\right]\mathrm{0},\frac{\pi}{\mathrm{2}}\right]\:\Rightarrow\:\mathrm{integrable}\:\mathrm{at}\:\mathrm{V}\left(\mathrm{0}\right)\:\mathrm{we}\:\mathrm{have} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\sim\frac{\mathrm{nx}}{\mathrm{x}}\:=\mathrm{n}\:\mathrm{so}\:\:\mathrm{I}_{\mathrm{n}} \mathrm{exist} \\ $$$$\left.\mathrm{2}\right)\mathrm{I}_{\mathrm{n}}…
Question Number 35117 by math1967 last updated on 15/May/18 $$\int\frac{\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{4}} −\mathrm{3}{x}−\mathrm{2}}{dx} \\ $$ Answered by MJS last updated on 16/May/18 $$\int\frac{\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{4}} −\mathrm{3}{x}−\mathrm{2}}{dx}=\int\frac{\mathrm{2}{x}+\mathrm{3}}{\left({x}^{\mathrm{2}} −{x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +{x}+\mathrm{2}\right)}{dx}= \\…
Question Number 166180 by mnjuly1970 last updated on 15/Feb/22 $$ \\ $$$$\:\:\:\:\:\:{prove}\:\:{that} \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}\:\right)}{{x}^{\:\mathrm{2}} }\:{dx}\:=\:\mathrm{2}\:\zeta\:\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:−−−{proof}−−− \\ $$$$\:\:\:\:\boldsymbol{\phi}=\:\left[\frac{−\mathrm{1}}{{x}}\:{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}\right)\:\right]_{\mathrm{0}} ^{\mathrm{1}} −\int_{\mathrm{0}}…
Question Number 35101 by ajfour last updated on 15/May/18 $${Find}\:{volume}\:{enclosed}\:{by} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{{c}^{\mathrm{2}} }=\mathrm{1}\:\:. \\ $$ Commented by behi83417@gmail.com last updated…
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Question Number 100606 by Dwaipayan Shikari last updated on 27/Jun/20 $$\int{e}^{{ix}^{{ix}…\infty} } {dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com