[url=https://en.wikipedia.org/wiki/Antiderivative]Antiderivative[/url], inverse derivative, primitive function or indefinite integral[sup] [/sup]of a [url=https://en.wikipedia.org/wiki/Function_(mathematics)]function[/url] [i]f[/i] is a [url=https://en.wikipedia.org/wiki/Differentiable_function]differentiable function[/url] [i]F[/i] whose [url=https://en.wikipedia.org/wiki/Derivative]derivative[/url] is equal to the original function [i]f[/i]. This can be stated symbolically as [i]F' [/i] = [i]f[/i].[br]Antiderivatives are related to [url=https://en.wikipedia.org/wiki/Integral]definite integrals[/url] through the [url=https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus]fundamental theorem of calculus[/url]: the definite integral of a function over an [url=https://en.wikipedia.org/wiki/Interval_(mathematics)]interval[/url] is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.[br][center][math]\int_a^bf\left(x\right)dx=F\left(b\right)-F\left(a\right)[/math] [/center]For lists of antiderivatives of primitive functions, see [url=https://en.wikipedia.org/wiki/Lists_of_integrals]lists of integrals[/url].

Drag the blue point [color=#76a5af][i]x[/i][/color] to change the upper limit of the definite integral. Observe how the area changes with [color=#1e84cc][i]x[/i][/color].

Integrfal from 0 to ∞ could be finite un infinite value. Using the Newton-Leibniz formula and finding the limiting value for upper boundary give us: [br][center][br][math]\int_0^{\infty}\frac{1}{e^x}dx=\lim_{x\rightarrow\infty}\left(-\frac{1}{e^x}\right)-\left(-1\right)=1[/math][/center]