Table of Integrals, Series, and Products, 8th Edition

2.5–2.6 Trigonometric Functions

2.50 Introduction

2.501 Integrals of the form ${\displaystyle \int R\left(\text{sin }x,\text{cos }x\right)\text{d}x}$ can always be reduced to integrals of rational functions by means of the substitution $t\text{ = tan}\frac{x}{2}$.

2.502 If $R\text{(sin }x\text{, cos }x\text{)}$ satisfies the relation $R\text{(sin }x\text{, cos }x\text{) = }-R\text{(}-\text{sin }x\text{, cos }x\text{) ,}$it is convenient to make the substitution $t\text{=}\text{cos}x\text{.}$

2.503 If this function ...