Integrals

The following general rules can be applied to all integrations, where f() and g() are functions.

( n f(x) ) dx	=	n f(x) dx
( f(x) + g(x) ) dx	=	f(x) dx + g(x) dx
( f(x) g(x) ) dx	=	f(x) g(x) dx - (d/dx( f(x) ) g(x) dx) dx

Integrals of Common Functions

Function F(x) = y	Integral   y dx
xn	1/(n + 1) xn+1
1/x	Ln x
eax	1/a eax
Ln x	x Ln x - x
Logax	x Loga (x / e)
sin ax	-1/a cos ax
cos ax	1/a sin ax
tan ax	-1/a Ln (cos ax)
cosec x	Ln(cosec x - cot x)
sec x	Ln( sec x + tan x)
cot x	Ln sin x
arcsin(x/a)	x arcsin(x/a) + Ö ( a2 - x2)
arccos(x/a)	x arccos(x/a) - Ö( a2 - x2)
arctan(x/a)	x arctan(x/a) - a Ln Ö( a2 + x2)