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

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2.57 Integrals containing a±bsinxsi1545_e or a±bcosxsi1546_e

Notation:

α=arcsin1sinx2,β=arcsinb(1sinx)a+b,γ=arcsinb(1cosx)a+b,δ=arcsin(a+b)(1cosx)2(abcosx),r=2ba+bsi1547_e

2.571

1. 

dxa+bsinx=2a+bF(α,γ)[ a>b>0, π2x<π2]=2bF(β,1γ)[ 0<| a|<b, arcsinab<x<π2]

si1548_e

BY (288.00, 288.50)

2. 

sinx dxa+bsinx=2aba+bF(α,γ)2a+bbE(α,γ) [ a>b>0, π2x<π2] =2b{ F(β,1γ)2E(β,1

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