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)

 

 
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