Algebra Questions

Question Number 206773 by MaruMaru last updated on 24/Apr/24

$$\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{x}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{dx}= \\$$$${I}^{\mathrm{2}} =\int\int_{\:\boldsymbol{\mathcal{D}}} \:\frac{{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \left({y}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{dA} \\$$$${x}={r}\mathrm{cos}\left(\theta\right)\:\:{y}={r}\mathrm{sin}\left(\theta\right) \\$$$${J}=\mid\frac{\partial\left({x},{y}\right)}{\partial\left({r},\theta\right)}\mid{drd}\theta={rdrd}\theta \\$$$$\int\int_{\:\boldsymbol{\mathcal{D}}} \:\frac{{re}^{−{r}^{\mathrm{2}} } }{\left({r}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \left(\theta\right)+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \left({r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \left(\theta\right)+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{drd}\theta \\$$

Commented by MaruMaru last updated on 24/Apr/24

$${next}...??? \\$$

Commented by Frix last updated on 24/Apr/24

$$\mathrm{Differnt}\:\mathrm{paths}\:\mathrm{see}\:\mathrm{question}\:\mathrm{206549} \\$$

Commented by MaruMaru last updated on 25/Apr/24

$${wow}\:{thx} \\$$