Question Number 57819 by behi83417@gmail.com last updated on 12/Apr/19 $$\boldsymbol{\mathrm{a}}.\:\:\int\:\:\:\left[\frac{\mathrm{1}−\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}+\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} }\right]\:^{\frac{\mathrm{1}}{\mathrm{2}}} \:\boldsymbol{\mathrm{dx}}=? \\ $$$$\boldsymbol{\mathrm{b}}.\:\:\:\:\:\int\:\:\frac{\boldsymbol{\mathrm{lnx}}}{\:\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}}}=? \\ $$$$\boldsymbol{\mathrm{c}}.\:\:\:\:\:\:\:\underset{\:\sqrt{\boldsymbol{\mathrm{e}}}} {\overset{\:\:\:\:\:\boldsymbol{\mathrm{e}}} {\int}}\:\:\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{lnx}}\right)\boldsymbol{\mathrm{dx}}=? \\ $$ Commented by Abdo msup.…
Question Number 123352 by aristarque last updated on 25/Nov/20 $$\int\frac{{e}^{{x}} }{{x}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 57817 by Abdo msup. last updated on 12/Apr/19 $$\:{find}\:{the}\:{value}\:{of}\:\:\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dx}}{\:\sqrt{\mathrm{2}{cos}^{\mathrm{2}} {x}\:+\mathrm{3}{sin}^{\mathrm{2}} {x}}} \\ $$ Commented by mr W last updated on 13/Apr/19…
Question Number 188861 by Shlock last updated on 08/Mar/23 Answered by cortano12 last updated on 08/Mar/23 $$\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\mathrm{x}\:\mathrm{d}\left(\mathrm{f}\:'\left(\mathrm{x}\right)\right)=\:\left[\:\mathrm{x}\:\mathrm{f}\:'\left(\mathrm{x}\right)−\mathrm{f}\left(\mathrm{x}\right)\:\right]_{\mathrm{0}} ^{\mathrm{4}} \\ $$$$\:=\:\left[\mathrm{4}\:\mathrm{f}\:'\left(\mathrm{4}\right)−\mathrm{f}\left(\mathrm{4}\right)+\mathrm{f}\left(\mathrm{0}\right)\right] \\ $$$$\:=\:\mathrm{4}.\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{2}+\mathrm{3}\:=\:\mathrm{3}\: \\…
Question Number 123331 by 676597498 last updated on 24/Nov/20 $$\int\:\frac{{sinx}}{{x}}\:{dx} \\ $$ Answered by MJS_new last updated on 25/Nov/20 $$\int\frac{\mathrm{sin}\:{x}}{{x}}{dx}=\mathrm{Si}\:\left({x}\right)\:+{C} \\ $$$$\mathrm{Si}\:\left({x}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{Integral}\:\mathrm{Sinus}.\:\mathrm{search}\:\mathrm{for}\:\mathrm{it}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{www} \\…
Question Number 57749 by maxmathsup by imad last updated on 11/Apr/19 $${find}\:\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{\mathrm{9}+{x}^{\mathrm{2}} }} \\ $$ Commented by maxmathsup by imad last updated on 11/Apr/19…
Question Number 57750 by maxmathsup by imad last updated on 11/Apr/19 $${find}\:\int\:{x}^{\mathrm{2}} \sqrt{\mathrm{25}−{x}^{\mathrm{2}} }{dx}\: \\ $$ Answered by MJS last updated on 11/Apr/19 $$\int{x}^{\mathrm{2}} \sqrt{\mathrm{25}−{x}^{\mathrm{2}}…
Question Number 57748 by maxmathsup by imad last updated on 11/Apr/19 $${find}\:\int\:{x}^{\mathrm{2}} \sqrt{\mathrm{4}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on 11/Apr/19…
Question Number 57746 by maxmathsup by imad last updated on 10/Apr/19 $${let}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{xt}\:+\mathrm{1}\right)^{\mathrm{2}} }\:\:{with}\:\mid{x}\mid<\mathrm{1}\:\:\:\left({x}\:{real}\right) \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{tdt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{xt}\:+\mathrm{1}\right)^{\mathrm{3}} } \\…
Question Number 123261 by mnjuly1970 last updated on 24/Nov/20 $$\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\Omega=\int_{\mathbb{R}} {e}^{{x}−{sinh}^{\mathrm{2}} \left({x}\right)} {dx}=\sqrt{\pi} \\ $$ Answered by Olaf last…