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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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3.72–3.74 Combinations of trigonometric and rational functions

3.721

1. 

0sin(ax)xdx=π2signa

si2809_e  FI II 645

2. 

1sin(ax)xdx=si(a)

si2810_e  BI 203(5)

3.8 

1cos(ax)xdx=ci(a)

si2811_e  BI 203(5)

3.722

1. 

0sin(ax)x+bdx=ci(ab)sin(ab)cos(ab)si(ab)[|argb|<π,a>0]

si2812_e  BI(16)(1), FI II 646a

2.11 

sin(ax)x+bdx=πeiab[a>0, Imb>0]

3. 

0cos(ax)x+bdx=sin(a

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