Section 1

Notation, domains and conventions

$C$ represents a real constant of integration.
We use $sin x$ for sine.
$arcsin x$ , $arccos x$ , $arctan x$ , and $arcsec x$ represent inverse functions, not reciprocals.
$csc x = 1/ sin x$ , $sec x = 1/ cos x$ , and $cot x = cos x / sin x$ .
In an indefinite integral, two antiderivatives that differ by a constant represent the same family.
Every formula should be applied only where the integrand is defined.
In real expressions: - $ln x$ requires $x > 0$ , while $ln ∣ x ∣$ allows $x \neq = 0$ . - $g (x)$ requires $g (x) \geq 0$ . - If a radical is in the denominator, $g (x) > 0$ is required. - Every denominator must be nonzero.
For $a^{x}$ , we assume $a > 0$ ; if $1/ ln a$ appears, also $a \neq = 1$ .
In formulas with $a^{2} \pm x^{2}$ , we normally take $a > 0$ .