Question

$\underset{-a}{\overset{a}{\int }}\frac{x{e}^{x^2}}{1+x^2}dx$

Answer 1

$$\begin{gathered} {\int }_{-a}^a\frac{x{e}^{x^2}}{1+x^2}dx \\ \mathrm{Let}f\left(x\right)=\frac{x{e}^{x^2}}{1+x^2} \\ \mathrm{Consider}f\left(-x\right)=-\frac{x{e}^{x^2}}{1+x^2}=-f\left(x\right) \\ \mathrm{Thus}f\left(x\right)i\mathrm{s}\mathrm{an}\mathrm{odd}\mathrm{function} \\ \mathrm{Therefore}, \\ {\int }_{-a}^a\frac{x{e}^{x^2}}{1+x^2}dx=0 \end{gathered}$$ode is 4430. →