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I believe the questioner means e^(-x^2), which is perhaps the most famous of many functions which do not have anti-derivatives which can be expressed by elementary functions. The definite integral from minus infinity to plus infinity, however, is known: It is sqrt(pi).
The antiderivative to e^(-2x) is, (-*e^(-2x)/2)
Though the anti-derivative (integral) of many functions cannot be expressed in elementary forms, a variety of functions exist only as solutions to certain "unsolvable" integrals. the equation erf(x), also known as the error function, equals (2/sqrt(pi))*integral e(-t^2) dt from 0 to x. As mentioned before, this cannot be expressed through basic mathematical functions, but it can be expressed as an infinite series.
If the question is the antiderivative of e - x2, the answer is e*x - x3/3
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What is the antiderivative of zero?
The antiderivative of a function which is equal to 0 everywhere is a function equal to 0 everywhere.
What is the fundamental theory of calculus?
The fundamental theorum of calculus states that a definite integral from a to b is equivalent to the antiderivative's expression of b minus the antiderivative expression of a.
What is the antiderivative of e to the -x?
-e-x + C.
How can you calculate the arbitrary constant in the solution to an antiderivative?
You can't, unless it's an initial value problem. If f(x) is an antiderivative to g(x), then so is f(x) + c, for any c at all.
What is the anti derivative of the square root of 1-x2?
-1
