3.72–3.74 Combinations of trigonometric and rational functions

3.721

1.

${\int }_{0}^{\infty }\frac{\text{sin}\left(ax\right)}{x}\text{d}x=\frac{\pi }{2}\text{sign}a$ FI II 645

2.

${\int }_{1}^{\infty }\frac{\text{sin}\left(ax\right)}{x}\text{d}x=-\text{si}\left(a\right)$ BI 203(5)

3.8

${\int }_{1}^{\infty }\frac{\text{cos}\left(ax\right)}{x}\text{d}x=-\text{ci}\left(a\right)$ BI 203(5)

3.722

1.

${\int }_{0}^{\infty }\begin{array}{ll}\frac{\text{sin}\left(ax\right)}{x+b}\text{d}x=\text{ci}\left(ab\right)\text{sin}\left(ab\right)-\text{cos}\left(ab\right)\text{si}\left(ab\right)\hfill & \left[|\text{arg}b|<\pi ,a>0\right]\hfill \end{array}$ BI(16)(1), FI II 646a

2.11

3.

$\begin{array}{l}{\int }_{0}^{\infty }\frac{\text{cos}\left(ax\right)}{x+b}\text{d}x=-\text{sin}\left(a\hfill \end{array}$

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