Gregg said:what level is this at?
Cyosis said:I don't think that integral is going to be possible without special functions.
Cyosis said:Where did you get get this integral from and what is the question? Finding a 'normal' anti-derivative is not going to happen. So if this is a calculus one exercise there is more to it than you're telling us.
Cyosis said:I see, while you may think this integral is nearly the same it is in fact much much easier. Just do the division and you get three trivial expressions.
Cyosis said:The method is correct, but the arithmetic is not. For example 1/2-1/4 is not -1/8 and 2/3-1/4 is not -1/6.
An antiderivative, also known as the primitive or indefinite integral, is the reverse operation of differentiation. It is a function whose derivative is the original function.
An antiderivative does not have any specific limits of integration, while a definite integral has both an upper and lower limit. This means that an antiderivative represents a family of functions, while a definite integral represents a single value.
No, not all functions have an antiderivative that can be expressed using elementary functions. Some functions, like e^x or sin(x^2), do not have an antiderivative that can be written in terms of common functions. These functions are called non-elementary functions.
To find the antiderivative of a function, you can use the reverse rules of differentiation. For example, if the original function is 2x, the antiderivative would be x^2 + C, where C is a constant. You can also use integration techniques such as substitution or integration by parts.
The constant of integration, represented by C, is added to the antiderivative because when a function is differentiated, the constant disappears. This means that there are multiple antiderivatives for a given function, but they all differ by a constant. The constant of integration is necessary to account for all possible antiderivatives.