given the function
$$ \int _{0}^{\infty}\sqrt{x}exp(-x) $$
can we use Pade approximants to integrate this i mean let bhe te rational approxsiamtions of
$ \sqrt{x}= \frac{A(x)}{B(x)} $ and $ exp(-x)= \frac{C(x)}{D(x)} $
cna i simply evaluate (aproximation) the integral with this ?
$$ \int _{0}^{\infty}\sqrt{x}exp(-x) = \int _{0}^{\infty}\frac{A(x) C(x)}{B(x) D(x)}$$
and the simply do the integration witht eh integrad $ \frac{A(X)C(x)}{B(x)D(x)} $