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z-r-cos-i-sin-find-z-z-z-z-

Question Number 224739 by thetpainghtun_111 last updated on 30/Sep/25 $$\mathrm{z}\:=\:\mathrm{r}\:\left(\mathrm{cos}\:\theta\:+\:\mathrm{i}\:\mathrm{sin}\:\theta\right),\:\mathrm{find}\:\frac{\mathrm{z}}{\overset{−} {\mathrm{z}}}\:+\frac{\overset{−} {\mathrm{z}}}{\mathrm{z}}. \\ $$ Answered by Frix last updated on 30/Sep/25 $${z}={r}\mathrm{e}^{\mathrm{i}\theta} \:\Leftrightarrow\:\bar {{z}}={r}\mathrm{e}^{−\mathrm{i}\theta} \\…

1-tan-d-

Question Number 224714 by fantastic last updated on 28/Sep/25 $$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{tan}\:\theta}}\:{d}\theta \\ $$ Commented by Ghisom_ last updated on 29/Sep/25 $$\int\frac{{d}\theta}{\:\sqrt{\mathrm{tan}\:\theta}}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:\theta}\:\rightarrow\:{d}\theta=\mathrm{2cos}^{\mathrm{2}} \:\theta\:\sqrt{\mathrm{tan}\:\theta}\right] \\ $$$$=\mathrm{2}\int\frac{{dt}}{{t}^{\mathrm{4}}…

Question-224642

Question Number 224642 by Rogerkeyter last updated on 23/Sep/25 Answered by som(math1967) last updated on 24/Sep/25 $$\:\:\:\:\:{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{dx}}}{\mathrm{1}+\frac{\boldsymbol{{e}}^{\sqrt{\mathrm{1}−\boldsymbol{{x}}}} }{\boldsymbol{{e}}^{\sqrt{\boldsymbol{{x}}}} }} \\ $$$$\:\:\:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{e}}^{\sqrt{\boldsymbol{{x}}}}…

x-a-a-Z-0-a-Z-1-0-3-x-dx-

Question Number 224568 by fkwow344 last updated on 19/Sep/25 $$\sqrt{{x}}={a\begin{cases}{{a}\in\mathbb{Z}=\mathrm{0}}\\{{a}\notin\mathbb{Z}=\mathrm{1}}\end{cases}} \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{3}} \:\sqrt{{x}}{dx}=? \\ $$ Commented by Ghisom_ last updated on 19/Sep/25 $$\mathrm{what}\:\mathrm{does}\:\mathrm{this}\:\mathrm{mean}? \\…