Is there a way to compute the following integral numerically?,
$\int_0^{\infty}\left(-\frac{2 x \Gamma \left(\frac{1}{4}\right) \, _1F_3\left(\frac{1}{4};\frac{1}{2},\frac{3}{4},\frac{5}{4};\frac{x^4}{256}\right)}{\sqrt{\pi }}+x^2 \, _1F_3\left(\frac{1}{2};\frac{3}{4},\frac{5}{4},\frac{3}{2};\frac{x^4}{256}\right)+\sqrt{\frac{2}{\pi }} \Gamma \left(\frac{1}{4}\right) \Gamma \left(\frac{3}{4}\right)\right)dx$
We know that $-\frac{2 x \Gamma \left(\frac{1}{4}\right) \, _1F_3\left(\frac{1}{4};\frac{1}{2},\frac{3}{4},\frac{5}{4};\frac{x^4}{256}\right)}{\sqrt{\pi }}+x^2 \, _1F_3\left(\frac{1}{2};\frac{3}{4},\frac{5}{4},\frac{3}{2};\frac{x^4}{256}\right) \rightarrow -\sqrt{\frac{2}{\pi }} \Gamma \left(\frac{1}{4}\right) \Gamma \left(\frac{3}{4}\right)$ as $x \rightarrow \infty.$