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$\begin{array}{ll}{\int }_{0}^{\infty }\frac{{x}^{4n+3}{e}^{-px}}{{a}^{\text{4}}-{x}^{\text{4}}}\text{d}x\hfill & =\frac{\text{1}}{\text{4}}{a}^{\text{4}n}\left[{e}^{ap}\text{Ei}\left(-ap\right)+{e}^{-ap}\text{Ei}\left(ap\right)+\text{2}\text{ci}\left(ap\right)cosap+\text{2}\text{si}\left(ap\right)sinap\right]\hfill \\ -\frac{\text{1}}{{p}^{\text{4}n}}\sum _{k=1}^{n}\left(\text{4}n-\text{4}k+3\right)!{\left({a}^{\text{4}}{p}^{\text{4}}\right)}^{k-\text{1}}\hfill \end{array}$

BI (91) (25)

3.359

$\begin{array}{ll}{\int }_{-\infty }^{\infty }\frac{{\left(i-x\right)}^{n}{e}^{-ipx}}{{\left(i+x\right)}^{n}i+{x}^{\text{2}}}\text{d}x\hfill & ={\left(-\text{1}\right)}^{n-1}\text{2}\pi p{e}^{-p}{L}_{n-\text{1}}\left(\text{2}p\right)\hfill \\ =0\hfill \end{array}\begin{array}{l}\text{for}p>0;\hfill \\ \text{for}p<0.\hfill \end{array}$

ET I 118(2)

3.36–3.37 Combinations of exponentials and algebraic functions

3.361

1.8

${\int }_{0}^{u}\frac{{e}^{-qx}}{\sqrt{x}}\text{d}x=\sqrt{\frac{\pi }{q}}\Phi \left(\sqrt{qu}\right)\left[q>0\right]$

2.8

${\int }_{0}^{\infty }\frac{{e}^{-qx}}{\sqrt{x}}\text{d}x=\sqrt{\frac{\pi }{q}}\left[q>0\right]$

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