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

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4.38–4.41 Logarithms and trigonometric functions

4.381

1. 

01ln?x?sin?ax?dx=1a[C+ln?aci?(a)][a>0]

si1079_e  GW (338)(2a)

2. 

01ln?x?cos?ax?dx=1a[si(a)+π2][a>0]

si1080_e  BI (284)(2)

3. 

02πln?x?sin?nx?dx=1n[C+ln(2nπ)ci(2nπ)]

si1081_e  GW (338)(1a)

4. 

02πln?x?cos?nx?dx=1n[si(2nπ)+π2]

si1082_e  GW (338)(1b)

4.382

1.12 

0ln|x+axa|sin?bx?dx=πb?sin?ab?[a>0,?b>0]

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