Question Number 127772 by Bird last updated on 02/Jan/21 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dx}}{\left({cosx}\:+\mathrm{2}{sinx}\right)^{\mathrm{2}} } \\ $$ Answered by mathmax by abdo last updated on 02/Jan/21 $$\mathrm{I}\:=\int_{\mathrm{0}}…
Question Number 127775 by Bird last updated on 02/Jan/21 $${prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}} {lnxdx}=−\gamma \\ $$ Answered by Dwaipayan Shikari last updated on 02/Jan/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 62232 by aliesam last updated on 18/Jun/19 Commented by maxmathsup by imad last updated on 18/Jun/19 $${we}\:{have}\:\mid\alpha+\beta\:{e}^{{i}\theta} \mid\:=\mid\alpha\:+\beta{cos}\theta\:+{i}\beta{sin}\theta\mid\:=\sqrt{\left(\alpha+\beta{cos}\theta\right)^{\mathrm{2}} \:+\beta^{\mathrm{2}} {sin}^{\mathrm{2}} \theta}\:\Rightarrow \\ $$$${ln}\left(\mid\alpha+{ie}^{{i}\theta}…
Question Number 62227 by behi83417@gmail.com last updated on 17/Jun/19 $$\mathrm{1}.\int\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:\:}\boldsymbol{\mathrm{dx}}=? \\ $$$$\mathrm{2}.\int\:\:\:\frac{\sqrt{\mathrm{1}−\boldsymbol{\mathrm{tgx}}}}{\boldsymbol{\mathrm{sinx}}}\:\:\boldsymbol{\mathrm{dx}}=? \\ $$$$\mathrm{3}.\int\:\:\:\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} .\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)\boldsymbol{\mathrm{dx}}=? \\ $$$$\mathrm{4}.\int\:\:\frac{\boldsymbol{\mathrm{sinx}}}{\mathrm{1}+\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{x}}}\:\boldsymbol{\mathrm{dx}}=? \\ $$ Commented by maxmathsup…
Question Number 62220 by maxmathsup by imad last updated on 17/Jun/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{t}^{\mathrm{2}} }{{x}^{\mathrm{6}} \:\:+{t}^{\mathrm{6}} }\:{dt}\:\:\:\:\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{t}^{\mathrm{2}} }{\left({x}^{\mathrm{6}} \:+{t}^{\mathrm{6}}…
Question Number 62213 by maxmathsup by imad last updated on 17/Jun/19 $${calculate}\:\int\int\int_{{D}} \:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} }{dxdydz}\:{with} \\ $$$${D}\:=\left\{\left({x},{y},{z}\right)\in{R}^{\mathrm{3}} \:/\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}\:\:{and}\:\:\:\mathrm{2}\leqslant{z}\leqslant\mathrm{3}\:\right\} \\ $$ Commented…
Question Number 62208 by maxmathsup by imad last updated on 17/Jun/19 $${find}\:{f}\left({a}\right)\:=\int\:\:\left({x}−{a}\right)\sqrt{{x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on 18/Jun/19…
Question Number 62209 by maxmathsup by imad last updated on 17/Jun/19 $${find}\:{g}\left({a}\right)\:=\int\left({x}+{a}\right)\sqrt{{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }{dx}\: \\ $$ Commented by maxmathsup by imad last updated on 18/Jun/19…
Question Number 62207 by maxmathsup by imad last updated on 17/Jun/19 $${calculate}\:\int\:\:\:\:\:\:\frac{{x}+\mathrm{3}}{\left({x}−\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}\:{dx} \\ $$ Commented by maxmathsup by imad last updated on 18/Jun/19 $${I}\:=\int\:\frac{{x}−\mathrm{2}\:+\mathrm{5}}{\left({x}−\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}}…
Question Number 62203 by maxmathsup by imad last updated on 17/Jun/19 $${calculate}\:\int\int_{\left[\mathrm{0},\mathrm{2}\right]^{\mathrm{2}} } \:\:\:\:\frac{{arctan}\left(\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right)}{\mathrm{3}−\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }}{dxdy} \\ $$ Commented by maxmathsup by imad…