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

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3.78–3.81 Rational functions of x and of trigonometric functions

3.781

1. 

0(sinxx11+x)dxx=1C(cf.3.7844and3.7812)

si3130_e  BI (173)(7)

2. 

0(cosx11+x)dxx=C

si3131_e  BI (173)(8)

3.782

1. 

0u1cosxxdxucosxxdx=C+lnu[u>0]

si3132_e  GW (333)(31)

2. 

01cosaxx2dx=aπ2[a0]

si3133_e  BI (158)(1)

3.12 

1cosxx(xb)dx=πib(eib1)[Imb0,Reb20]

  ET II 253(48)

3.783 ...

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