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${\int }_{0}^{\infty }cos{\left(ax-\frac{b}{x}\right)}^{2}\frac{\text{d}x}{{x}^{2}}=\frac{\sqrt{2\pi }}{4b}$

BI (179)(14)a

[a >; 0, b > 0]

3.875

1.

${\int }_{u}^{\infty }\frac{xsin\left(p\sqrt{{x}^{2}-{u}^{2}}\right)}{{x}^{2}+{a}^{2}}cosbx\text{d}x=\frac{\pi }{2}\mathrm{exp}\left(-p\sqrt{{a}^{2}+{u}^{2}}\right)coshab$

ET I 27(39)

[0 < b < p]

2.

${\int }_{u}^{\infty }\frac{xsin\left(p\sqrt{{x}^{2}-{u}^{2}}\right)}{{a}^{2}+{x}^{2}-{u}^{2}}cosbx\text{d}x=\frac{\pi }{2}{e}^{-ap}\left(b\sqrt{{u}^{2}-{a}^{2}}\right)$

ET I 27(38)

[0 < b < p, a < 0]

3.12

${\int }_{0}^{\infty }\frac{sin\left(p\sqrt{{a}^{2}+{x}^{2}}\right)}{{\left({a}^{2}+{x}^{2}\right)}^{2}}cosbx\text{d}x=\frac{\pi p}{2a}{e}^{-ap}$

ET I 26(29)

[0 < p < b, b >; a >; 0]

4.*

${\int }_{0}^{\infty }\frac{sin\left(p\sqrt{{x}^{2}+{a}^{2}}\right)}{{\left({x}^{2}+{a}^{2}\right)}^{2}}cos\left(bx\right)\text{d}$

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