Q:

# What is the antiderivative formula?

A:

There's no single formula to use to find the antiderivative, so an antiderivative formula, per se, doesn't exist. However, there are rules (which in most cases need to be memorized) that can be used to find the antiderivative. Some of those rules are listed below.

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1. The derivative of a constant is 0. A constant is any number that exists on its own without a variable. Therefore 3 is a constant, but 3x is not. For example, the antiderivative of f(x) = x^2dx is F(X) = X^3/3 + C. It is necessary to add the C because there's no way of knowing exactly what number is in the place of the C, but it is known that it's possible for a number to exist there.

2. The Power Rule: Used when finding the antiderivative of a function whose variable has an exponent. So for x^n, as long as n is not equal to -1, the antiderivative is x^(n+1)/ (n + 1)+ C. For example, the antiderivative of f(x)= x^9dx, = F(X) x^10/10 +C.

3. Exponent rule: Used when taking the antiderivative of function containing e. The antiderivative of an exponent function is that same exponent function, so the antiderivative of e^xdx = e^x+C. For example, the antiderivative of e^5dx = e^5+C.

4. Logarithm Rule: Used to find the antiderivative of a function raised to the -1 power. The antiderivative of a logarithm function is the natural log(ln) of the absolute value of that function. So the antiderivative of x^-1dx = ln |x| +C.

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