3.64–3.65 Powers and rational functions of trigonometric functions

3.641

1. 

0π/2sinp1xcospxacosx+bsinxdx=0π/2sinpxcosp1xasinx+bcosxdx=πcos?ecpπa1pbp

si2462_e  GW (331)(62)

[ab > 0, 0 < p < 1]

2. 

0π/2sin1pxcospx(sinx+cosx)3?dx=0π/2sinpxcos1px(sinx+cosx)3dx=(1p)p2πcosecpπ

si2463_e  BI(48)(5)

[-1 < p < 2]

3.642

1. 

0π/2sin2μ1xcos2ν1xdx(a2sin2x+b2cos2x)μ+ν?=12a2μb2νB(μ,ν)[Reμ>0,  Reν>0]

si2464_e  BI (48)(28)

2. 

0π/2sinn1xcosn1xdx(a2cos2x+b2sin2x)

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