What Is the Antiderivative of E2x?
The antiderivative of e^(2x) is (e^(2x))/2 + c, where c is an arbitrary constant. The antiderivative of a function is more commonly called the indefinite integral.
An antiderivative of a general function, f(x), is a function that can be differentiated with respect to x to give f(x). The general result for the antiderivative must contain an arbitrary constant, c, because all constants differentiate to zero. By substituting minimum and maximum values for x into the antiderivative, one can compute a definite integral from this result. It is straightforward to show that (e^(2x))/2 + c differentiates to e^(2x) by using the general rule that e^(f(x)) differentiates to f'(x)e^(f(x)), where f'(x) is the derivative of f(x) with respect to x.