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

2

Indefinite Integrals of Elementary Functions

2.0 Introduction

2.00 General remarks

We omit the constant of integration in all the formulas of this chapter. Therefore, the equality sign (=) means that the functions on the left and right of this symbol differ by a constant. For example (see integral 2.01 15), we write

$\int \frac{\text{d}x}{1+x^2}=\arctan x=-\text{arccot}x$

although

$\text{arctan}x=-\text{arccot}x\pm \frac{\pi }{2}$

When we integrate certain functions, we obtain the logarithm of the absolute value $(\text{for}\text{example}{\displaystyle \int \frac{\text{d}x}{\sqrt{1\text{+}{x}^2}}=ln\left|x\text{+}\sqrt{1+x^2}\right|}).$ In such formulas, the absolute-value ...