Indefinite Integrals
We use the symbol
∫ f(x) dx
called the indefinite integral, to represent the family of all antiderivatives of f(x), and we write:
∫ f(x) dx = F(x) + CifF'(x) = f(x)
- The symbol ∫ is called an integral sign.
- The function f(x) is called the integrand.
- The arbitrary constant C is called the constant of integration.
Indefinite Integrals of Basic Functions
For C a constant:
- ∫ xn dx = xn+1/(n + 1) + C, n ≠ -1
- ∫ ex dx = ex + C
- ∫ 1/x dx = ln |x| + C, x ≠ 0
Properties of Indefinite Integrals
For k a constant:
- ∫ k f(x) dx = k ∫ f(x) dx
- ∫ [f(x) ± g(x)] dx = ∫ f(x) dx ± ∫ g(x) dx