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

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3.82–3.83 Powers of trigonometric functions combined with other powers

3.821

1. 

0πxsinpxdx=π22p+1Γ(p+1)[Γ(p2+1)]2

si3325_e  BI(218)(7), LO V 121(71)

[p > −1]

2. 

0rπxsinnxdx=π22(2m1)!!(2m)!!r2[n=2m]=(1)r+1π(2m)!!(2m+1)!!r[n=2m+1]

si3326_e  GW (333)(8c)

[r is a natural number]

3.11 

0π/2xcosnxdx=π28(n1)!!(n)!!12n2k=0,mk oddm1(nk)1(n2k)2[n=2m]=π2(n1)!!(n)!!12n1k=0m1(nk)1(n2k)2[n=2m1]

si3327_e  GW (333)(9b)

4. 

0πxcos2mxdx=π22(2m1)!!(2m)!!

  BI (218)(10) ...

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