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

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3.926 Trigonometric functions of more complicated arguments combined withexponentials

3.9216

1.12 

0eγcosax2(cosγxsinγx)dx=π8aexp(γ22a)

si3781_e  ET | 26(28)

[a > 0, Re γ ≥ |Im γ|]

2.10 

0π/4Πn=1exp[1ntan2nx]=π21

si3782_e

3.10 

0π/2exp[n=11nsin2nx]=0π/2exp[n=11ncos2nx]=π4

si3783_e

3.922

1. 

0eβx2sinax2dx=12eβx2sinax2dx=π8β2+a2ββ2+a2=π2β2+a24sin(12arctanaβ)

  FI II 750, BI (263)(8)

[Reβ > 0, a>0]

2. 

0eβx2cosax2dx=12eβx2cosax2dx=

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