Question Number 206550 by SANOGO last updated on 18/Apr/24 $${calcul}\:\:{Residus}\:{de}\:{f}\:{en}\:{o} \\ $$$${f}\left({z}\right)=\frac{{ze}^{{z}} }{\left({z}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by Berbere last updated on 18/Apr/24 $${f}\:\:{n}'{a}\:{pas}\:{de}\:{poles}\:{en}\:\mathrm{0};{Res}\left({f},\mathrm{0}\right)=\mathrm{0} \\…
Question Number 206572 by mr W last updated on 18/Apr/24 Commented by mr W last updated on 18/Apr/24 $${radius}\:{of}\:{circles}\:{is}\:\mathrm{1}. \\ $$$${find}\:{AB}=? \\ $$ Answered by…
Question Number 206541 by luciferit last updated on 18/Apr/24 Answered by lepuissantcedricjunior last updated on 18/Apr/24 $$\int\frac{\mathrm{3}\boldsymbol{{x}}+\mathrm{5}}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{10}\boldsymbol{{x}}+\mathrm{51}}}\boldsymbol{{dx}}=\boldsymbol{{k}} \\ $$$$\boldsymbol{{k}}=\frac{\mathrm{3}}{\mathrm{2}}\int\frac{\mathrm{2}\boldsymbol{{x}}−\mathrm{5}+\frac{\mathrm{10}}{\mathrm{3}}+\mathrm{5}}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{10}\boldsymbol{{x}}+\mathrm{51}}}\boldsymbol{{dx}} \\ $$$$\boldsymbol{{k}}=\mathrm{3}\sqrt{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{10}\boldsymbol{{x}}+\mathrm{51}}+\frac{\mathrm{25}}{\mathrm{2}}\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\left(\boldsymbol{{x}}−\mathrm{5}\right)^{\mathrm{2}} +\mathrm{26}}}…
Question Number 206542 by luciferit last updated on 18/Apr/24 Answered by lepuissantcedricjunior last updated on 18/Apr/24 $$\int\left(\mathrm{3}\boldsymbol{{x}}+\mathrm{5}\right)\boldsymbol{{arctan}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}}=\boldsymbol{{k}} \\ $$$$\begin{cases}{\boldsymbol{{u}}=\boldsymbol{{arctan}}\left(\boldsymbol{{x}}\right)}\\{\boldsymbol{{v}}'=\left(\mathrm{3}\boldsymbol{{x}}+\mathrm{5}\right)}\end{cases}=>\begin{cases}{\boldsymbol{{u}}'=\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }}\\{\boldsymbol{{v}}=\frac{\mathrm{3}}{\mathrm{2}}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\boldsymbol{{x}}}\end{cases} \\ $$$$\boldsymbol{{k}}=\left(\frac{\mathrm{3}}{\mathrm{2}}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\boldsymbol{{x}}\right)\boldsymbol{{arctan}}\left(\boldsymbol{{x}}\right)−\frac{\mathrm{3}}{\mathrm{2}}\int\frac{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}+\frac{\mathrm{10}}{\mathrm{3}}\boldsymbol{{x}}−\mathrm{1}}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}}…
Question Number 206543 by luciferit last updated on 18/Apr/24 Answered by lepuissantcedricjunior last updated on 18/Apr/24 $$\int\frac{\mathrm{3}+\mathrm{2}\sqrt{\boldsymbol{{x}}}}{\mathrm{4}+\sqrt{\boldsymbol{{x}}}}\boldsymbol{{dx}}=\int\frac{\mathrm{2}\left(\mathrm{4}+\sqrt{{x}}\right)−\mathrm{5}}{\mathrm{4}+\sqrt{\boldsymbol{{x}}}}\boldsymbol{{dx}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}\boldsymbol{{x}}−\left\{\mathrm{5}\int\frac{\boldsymbol{{dx}}}{\mathrm{4}+\sqrt{\boldsymbol{{x}}}}\:\:\:\:\boldsymbol{{x}}=\boldsymbol{{t}}^{\mathrm{2}} \Leftrightarrow\boldsymbol{{dx}}=\mathrm{2}\boldsymbol{{tdt}}\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:=\mathrm{2}\boldsymbol{{x}}−\left\{\mathrm{10}\int\left(\mathrm{1}−\frac{\mathrm{4}}{\mathrm{4}+\boldsymbol{{t}}}\right)\boldsymbol{{dt}}\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:=\mathrm{2}\boldsymbol{{x}}−\mathrm{10}\sqrt{\boldsymbol{{x}}}+\mathrm{40}\boldsymbol{{ln}}\left(\mathrm{4}+\sqrt{\boldsymbol{{x}}}\right)+\boldsymbol{{c}} \\…
Question Number 206568 by universe last updated on 18/Apr/24 Answered by Berbere last updated on 19/Apr/24 $$\frac{{x}}{{n}}={y}\:\:{A}\left({n}\right)=\int_{\mathrm{0}} ^{{n}} \left(\frac{\mathrm{2}{nx}}{{x}^{\mathrm{2}} +{n}^{\mathrm{2}} }\right)^{{n}} {dx}={n}\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\mathrm{2}{y}}{\mathrm{1}+{y}^{\mathrm{2}} }\right)^{{n}}…
Question Number 206536 by cortano21 last updated on 18/Apr/24 $$\:\:\:\:\underline{\underbrace{\lessdot}\cancel{} }\underbrace{\nsupseteqq\spadesuit\left[}\mathrm{2}^{{x}} \:\mathrm{sin}\:\left(\sqrt{\mathrm{4}−\mathrm{2}^{{x}+\mathrm{2}} }\:\right)\right. \\ $$ Commented by Frix last updated on 18/Apr/24 $$\mathrm{Simply}\:\mathrm{use}\:{t}=\sqrt{\mathrm{1}−\mathrm{2}^{{x}} } \\…
Question Number 206537 by necx122 last updated on 18/Apr/24 $$\int\frac{{x}^{\mathrm{4}} −\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}}{dx} \\ $$ Answered by Berbere last updated on 18/Apr/24 $$=\int\frac{{x}\left(\mathrm{4}{x}^{\mathrm{3}} +\mathrm{2}{x}\right)−\mathrm{2}{x}^{\mathrm{4}}…
Question Number 206571 by mr W last updated on 19/Apr/24 Answered by cortano21 last updated on 19/Apr/24 $$\:\:\underline{\:} \\ $$ Commented by mr W last…
Question Number 206511 by naka3546 last updated on 17/Apr/24 Commented by mr W last updated on 17/Apr/24 $${i}\:{got}\:\mathrm{17178}. \\ $$ Commented by A5T last updated…