Assume u = u(x) is a differentiable function of x . If n = −1, d dx ( [u(x

Definition :
An antiderivative of a function f is a
function F such that F ′(x) = f (x).
The indefinite integral of any function f w.r.t.
Z
x , written
f (x) dx , denotes the most general antiderivative of f .
If F is any antiderivative of f , then
Z
f (x) dx = F (x) + C,
C constant.
Z
To integrate f means to find
f (x) dx.
Z
is the integral sign, f (x) is the integrand, C
is the constant of integration and x is the variable
of integration.
Basic integration formulas
1.
Z
k dx = k x + C, k constant
n+1
x
2. xn dx =
+ C, n 6= −1
n+1
Z
Z
Z
dx
1
−1
dx =
= ln x + C, x > 0
3. x dx =
x
x
Z
4. ex dx = ex + C
Z
5.
Z
6.
Z
k f (x) dx = k
Z
f (x) dx, k constant
f (x) ± g (x) dx =
Z
f (x) dx ±
Z
g (x) dx.