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

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2.55-2.56 Rational functions of the sine and cosine

2.551

1. 

A+Bsin x(a+bsinx)ndx=1(n1)(a2b2)[ (AbaB)cos x(a+bsinx)n1+(AaBb)(n1)+(aBbA)(n2)sinx(a+bsinx)n1dx] 

si1475_e

TI (358)aFor n=1:si1476_e

2. 

A+Bsin x(a+bsinx)ndx=Bbx+AbaBbdxa+bsinx

si1477_e

(see 2.551 3)TI (342)

3. 

dxa+b sinx=2a2b2arctanatanx2+ba2b2[ a2>b2]=1b2a2lnatanx2+bb2a2atanx2+b+b2a2[ a2<b2]

2.552

1. 

A+Bcos x(a+bsinx)ndx=B(n1)b(a+bsinx)n1+Adx(a+bsinx)n

For n=1:(see 2.552

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