Question Number 62252 by hovea cw last updated on 18/Jun/19 $$\int\mathrm{ln}\left(\mathrm{x}+\mathrm{1}\right)/\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right) \\ $$$$\mathrm{limit}\:=\left\{\:\mathrm{0}>\mathrm{2}\right\} \\ $$ Commented by maxmathsup by imad last updated on 18/Jun/19…
Question Number 62251 by hovea cw last updated on 18/Jun/19 $$\int\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4}\right)^{\mathrm{1}/\mathrm{2}} \mathrm{dx} \\ $$$$\mathrm{trig}\:\mathrm{substitution}\:\mathrm{only} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 127779 by Bird last updated on 02/Jan/21 $${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{+\infty} \frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} } \\ $$ Answered by Dwaipayan Shikari last updated on 02/Jan/21…
Question Number 127776 by Bird last updated on 02/Jan/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127774 by Bird last updated on 02/Jan/21 $${calculate}\:\:{u}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 02/Jan/21…
Question Number 127777 by Bird last updated on 02/Jan/21 $${explicite}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{{x}^{\mathrm{2}} −{x}+{a}}{dx} \\ $$$${with}\:\:\:{a}>\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Answered by mathmax by abdo last updated on…
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…