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

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3.6–4.1 Trigonometric Functions

3.61 Rational functions of sines and cosines and trigonometric functions of multiple angles

3.611

1. 

02π(1cosx)nsinnxdx=0

si2337_e  BI (68)(10)

2. 

02π(1cosx)ncosnxdx=(1)nπ2n1

si2338_e  BI (68)(11)

3. 

0π(cost+isintcosx)ndx=0π(cost+isintcosx)n1dx=πPn(cost)

si2339_e  EH I 158(23)a

3.612

1.12 

0πsinnxcosmxsinxdx=0for 0>nm;=πfor n>m>0,   if m +n is odd and positive=0for n>m>0,   if m+n is even

  LI (64)(3)

2.12 

0πsinn

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