# Category:Primitives

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This category contains results about Primitives in the context of Calculus.

Definitions specific to this category can be found in Definitions/Primitives.

### Primitive of Real Function

Let $F$ be a real function which is continuous on the closed interval $\left[{a \,.\,.\, b}\right]$ and differentiable on the open interval $\left({a \,.\,.\, b}\right)$.

Let $f$ be a real function which is continuous on the open interval $\left({a \,.\,.\, b}\right)$.

Let:

- $\forall x \in \left({a \,.\,.\, b}\right): F' \left({x}\right) = f \left({x}\right)$

where $F'$ denotes the derivative of $F$ with respect to $x$.

Then $F$ is **a primitive of $f$**, and is denoted:

- $\displaystyle F = \int f \left({x}\right) \, \mathrm d x$

## Subcategories

This category has the following 54 subcategories, out of 54 total.

### E

### I

### P

## Pages in category "Primitives"

The following 43 pages are in this category, out of 43 total.

### P

- Primitive of Composite Function
- Primitive of Constant
- Primitive of Constant Multiple of Function
- Primitive of Cosine Integral Function
- Primitive of Error Function
- Primitive of Exponential Function/General Result
- Primitive of Exponential Integral Function
- Primitive of Function of Constant Multiple
- Primitive of Function under its Derivative
- Primitive of Periodic Function
- Primitive of Pointwise Sum of Functions
- Primitive of Power
- Primitive of Sine Integral Function
- Primitives involving a squared minus x squared
- Primitives involving a squared minus x squared squared
- Primitives involving a x squared plus b x plus c
- Primitives involving Power of a squared minus x squared
- Primitives involving Power of x squared minus a squared
- Primitives involving Power of x squared plus a squared
- Primitives involving Root of a squared minus x squared
- Primitives involving Root of a squared minus x squared cubed
- Primitives involving Root of x squared minus a squared
- Primitives involving Root of x squared minus a squared cubed
- Primitives involving Root of x squared plus a squared
- Primitives involving Root of x squared plus a squared cubed
- Primitives involving x squared minus a squared
- Primitives involving x squared minus a squared squared
- Primitives involving x squared plus a squared
- Primitives involving x squared plus a squared squared
- Primitives of Functions involving a x + b and p x + q
- Primitives of Functions involving Power of Root of a x + b
- Primitives of Functions involving Root of a x + b
- Primitives of Functions involving Root of a x + b and p x + q
- Primitives of Functions involving Root of a x + b and Root of p x + q
- Primitives of Hyperbolic Functions
- Primitives of Rational Functions involving a x + b
- Primitives of Rational Functions involving a x + b cubed
- Primitives of Rational Functions involving a x + b squared
- Primitives of Rational Functions involving Power of a x + b
- Primitives of Trigonometric Functions
- Primitives which Differ by Constant