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

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2.66 Combinations of trigonometric functions and exponentials

2.661 eax sinp x cosq x dx=1a2 + (p + q)2{ eax sinp x cosq1 x[ a cos x + (p + q) sin x]paeax sinp1 x cosq1 x dx + (q  1)(p + q)eax sinp x cosq2 x dx}=1a2 + (p + q)2{ eax sinp1 x cosq x[ a sin x  (p + q) cos x]+qaeax sinp1 x cosq1 x dx + (p  1)(p + q)eax sinp2 x cosq x dx}=1a2 + (p + q)2{ eax sinp1 x cosq1 x[ a sin x cos x + q sin2 x  p cos2 x]+q(q  1)eax sinp x cosq2 x dx + p(p  1)eax sinp2 x cosq x dx}=1a2 + (p + q)2{ eax sinp1 x cosq1 x(a sin x cos x + q sin2 x  p cos2 x)+q(q  1)eax sinp2 x cosq2 x dx (q  p)(p + q  1)eax sinp2 x cosq x dx }=1a2 + (p + q)2{ eax sinp1 x cosq1 x(a sin x cos x + q sin2 x  p cos2 x)+p(p  1)eax sinp2 x cos ...

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