Question Number 35046 by math khazana by abdo last updated on 14/May/18 $${find}\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\:\mathrm{1}+{x}\:{sin}^{\mathrm{2}} {t}\right){dt}\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{sin}^{\mathrm{2}} {t}\right){dt} \\ $$ Terms of…
Question Number 35044 by math khazana by abdo last updated on 14/May/18 $$\left.\mathrm{1}\right){find}\:\int\:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}} \:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\:\:{dt} \\ $$ Commented by math khazana…
Question Number 35043 by math khazana by abdo last updated on 14/May/18 $${let}\:{t}>\mathrm{0}\:{and}\:{F}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{sin}\left({x}^{\mathrm{2}} \right)\:{e}^{−{tx}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx} \\ $$$${calculate}\:\frac{{dF}}{{dt}}\left({t}\right). \\ $$ Answered by…
Question Number 166093 by peter frank last updated on 13/Feb/22 Commented by Eulerian last updated on 13/Feb/22 $$ \\ $$ Commented by Eulerian last updated…
Question Number 100557 by Mikael_786 last updated on 27/Jun/20 $$\Omega=\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{e}^{{ax}} }{{e}^{{bx}} +\mathrm{1}}{dx},\:{b}>{a} \\ $$ Answered by mathmax by abdo last updated on 27/Jun/20…
Question Number 35015 by NECx last updated on 14/May/18 $$\int\frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{\mathrm{2}} }{dx} \\ $$ Answered by ajfour last updated on 14/May/18 $${I}\:=\frac{\mathrm{1}}{\mathrm{3}}\int\frac{\mathrm{3}{x}^{\mathrm{2}} {dx}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{\mathrm{2}}…
Question Number 35018 by ajfour last updated on 14/May/18 $$\int\int\int\frac{{dxdydz}}{\left({x}+{y}+{z}+\mathrm{1}\right)^{\mathrm{3}} }\:\:\:{bounded}\:{by}\:{the} \\ $$$${coordinate}\:{planes}\:{and}\:{the}\:{plane} \\ $$$${x}+{y}+{z}=\mathrm{1}\:. \\ $$ Answered by ajfour last updated on 14/May/18 $$\int_{\mathrm{0}}…
Question Number 100543 by mhmd last updated on 27/Jun/20 Commented by mr W last updated on 27/Jun/20 $$\left(\mathrm{1}\right) \\ $$$${y}^{\mathrm{2}} =\mathrm{4}+\mathrm{4}−\mathrm{2}{y} \\ $$$$\Rightarrow{y}^{\mathrm{2}} +\mathrm{2}{y}−\mathrm{8}=\mathrm{0} \\…
Question Number 100538 by mhmd last updated on 27/Jun/20 Commented by MJS last updated on 27/Jun/20 $${x}={X}? \\ $$$${dx}? \\ $$$${dX}? \\ $$ Terms of…
Question Number 34992 by MJS last updated on 14/May/18 $$\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{\mathrm{cos}\left({x}\right)}{\mathrm{1}+\mathrm{2sin}\left(\mathrm{2}{x}\right)}{dx} \\ $$ Commented by math khazana by abdo last updated on 14/May/18 $${let}\:{put}\:{I}\:=\:\int_{\mathrm{0}}…