Table of Integrals, Series, and Products, 8th Edition

$\left[\mathrm{Re}\beta >0,\mathrm{Re}\text{γ}>0,a>0\right]$

3.962

1. 

${\displaystyle {\int }_0^{\infty }\frac{\sqrt{\sqrt{{\gamma }^2+x^2}-\gamma }\exp \left(-\beta \sqrt{{\gamma }^2+x^2}\right)}{\sqrt{{\gamma }^2+x^2}}sinax\text{d}x=\sqrt{\frac{\pi }{2}}\frac{a\exp \left(-\gamma \sqrt{a^2+{\beta }^2}\right)}{\sqrt{{\beta }^2+a^2}\sqrt{\beta \sqrt{a^2+{\beta }^2}}}}$

  ET I 75(38)

$\left[\mathrm{Re}\beta >0,\mathrm{Re}\gamma >0,a>0\right]$

2. 

${\displaystyle {\int }_0^{\infty }\frac{x\exp \left(-\beta \sqrt{{\gamma }^2+x^2}\right)}{\sqrt{{\gamma }^2+x^2}\sqrt{\sqrt{{\gamma }^2+x^2}-\gamma }}cosax\text{d}x=\sqrt{\frac{\pi }{2}}\frac{\sqrt{\beta \sqrt{a^2+{\beta }^2}}}{\sqrt{a^2+{\beta }^2}}\exp \left[-\gamma \sqrt{a^2+{\beta }^2}\right]}$

  ET I 17(29)

$\left[\mathrm{Re}\beta >0,\mathrm{Re}\gamma >0,a>0\right]$

3.963

1. 

${\displaystyle {\int }_0^{\infty }{e}^{-{tan}^2{x}_{}}\frac{sin\; ...}{}}$