Exponential Functions | Fundamental Integration Formulas

There are two basic formulas for the integration of exponential functions.

1. $\displaystyle \int a^u \, du = \dfrac{a^u}{\ln a} + C, \,\, a > 0, \,\, a \neq 1$

2. $\displaystyle \int e^u \, du = e^u + C$

Where
$u$ = function, say $f(x)$
$a$ = constant (example: 3, π, sin 30°, √7)

$e = {\underset{x \to \infty}\lim} \left( x + \dfrac{1}{x} \right)^x$

$e = {\underset{x \to \infty}\lim} (1 + x)^{1/x}$

$e = 2.71828\,1828\,4590\,4...$

Submitted by Romel Verterra on February 21, 2010 - 11:02pm

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