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

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2.63–2.65 Products of trigonometric functions and powers

2.631

1. 

xr sinp x cosq x dx=1(p + q)2 [ (p + q)xr sinp+1 x cosq1 x                                                           + rxr1 sinp x cosq x  r(r1) xr2 sinp x cosq x dx                             rp xr1 sinp1 x cosq1 x dx + (q1) (p+q) xr sinp x cosq2 x dx]=1(p + q)2 [  (p + q)xr sinp1 x cosq+1 x                                                       +rxr1 sinp x cosq x  r(r1) xr2 sinp x cosq x dx                            + rp xr1 sinp1 x cosq1 x dx + (p1) (p+q) xr sinp2 x cosq x dx]

si1980_e

GU (331)(1)

2. 

xm sinn x dx=xm1 sinn1 xn2{ m sin x  nx cos ...

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