An antiderivative of a function f (x) is any function g(x) whose derivative is f (x). If g(x) is an antiderivative of f (x), then g(x) + C is another antiderivative. In fact, every antiderivative is of the form g(x) + C for some constant C.
The indefinite integral of f (x) is the
family of all antiderivatives of f (x) and is
denoted
f (x) dx.
To evaluate an indefinite integral
Evaluate
2x2 + 3x + 5
dx =
x3 +
x2 + 5x
You can evaluate indefinite integrals of piecewise-defined functions. The result will be a piecewise-defined function.