Category: Integration

Question Number 202592 by Calculusboy last updated on 30/Dec/23 $$\mathit{I}\mathit{f}{\mathit{I}}_{\mathit{n}}\mathit{d}\mathit{e}\mathit{n}\mathit{o}\mathit{t}\mathit{e}\mathit{s}\int {\mathit{z}}^{\mathit{n}}{\mathit{e}}^{\frac{1}{\mathit{z}}}\mathit{d}\mathit{z},\mathit{t}\mathit{h}\mathit{e}\mathit{n}\mathit{s}\mathit{h}\mathit{o}\mathit{w}\mathit{t}\mathit{h}\mathit{a}\mathit{t}$$$$(\mathit{n}+1)!{\mathit{I}}_{\mathit{n}}={\mathit{I}}_0+{\mathit{e}}^{\frac{1}{\mathit{z}}}(1\cdot !{\mathit{z}}^2+2\cdot !{\mathit{z}}^3+\cdot \cdot \cdot +\mathit{n}!\cdot {\mathit{z}}^{\mathit{n}+1})$$$$$$…

Question Number 202522 by mou0113 last updated on 28/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 202485 by Calculusboy last updated on 27/Dec/23 Commented by MathematicalUser2357 last updated on 28/Dec/23 $${\mathrm{Can}}^{\prime }\mathrm{t}\mathrm{integrate}\mathrm{in}\mathrm{range}[-\mathrm{\infty },\mathrm{\infty }]$$ Commented by TheHoneyCat last updated on…

Question Number 202418 by MathematicalUser2357 last updated on 26/Dec/23 $$\mathrm{Hard}\mathrm{integral}$$$$\int \int \int \int \int \int \int \int \int \left|\begin{array}{ccc}a& b& c\\ f& g& h\\ j& k& l\end{array}\right|dldkdjdhdgdfdcdbda=$$ Answered by Frix last updated on 26/Dec/23 $$\mathrm{Not}\mathrm{hard}\mathrm{at}\mathrm{all}$$$$=\frac{{abcfghjkl}}{\mathrm{8}}\left({a}\left({gl}−{hk}\right)−{b}\left({fl}−{hj}\right)+{c}\left({fk}−{gj}\right)\right) \…

Question Number 202406 by mou0113 last updated on 26/Dec/23 Answered by witcher3 last updated on 26/Dec/23 $$\mathrm{f}\left(\mathrm{s}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{t}^{\mathrm{s}} }{\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{dt}\Rightarrow\mathrm{f}'\left(\mathrm{0}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}}…