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The antiderivative calculator allows to calculate a primitive online with detail and calculation steps.

Antiderivative online

The **antiderivative calculator** allows to find primitive function, primitive integral or indefinite integral of a function using
integration properties and different calculation mechanisms online. The antiderivative calculator is able to do symbolic **antidifferentiation**.

The antiderivative calculator allows to **integrate online** any polynomial.

For example, **to compute an antiderivative** of the polynomial following `x^3+3x+1`, you must enter
antiderivative(x^3+3x+1;x), after calculating the result
`(3*x^2)/2+(x^4)/4+x` is returned.

The antiderivative calculator is able **to calculate online** all **antiderivatives** of **usual functions** : sin, cos, tan, ln, exp, sh, th, sqrt (square root), and many more ...

So, to obtain an antiderivative of the cosine function with respect to the variable x, type, antiderivative(cos(x);x), result `sin(x)` is returned after calculation..

Integration is a linear function, using this property allows the function to get the required result.

For the **online calculation** of **antiderivative** of **function sum**,
simply type the mathematical expression that contains the sum, specify the variable and apply function .

For example, to calculate an antiderivative line of the sum of the following functions `cos(x)+sin(x)`type antiderivative(cos(x)+sin(x);x), after calculating the result `sin(x)-cos(x)` is returned.

**To calculate** **online** an **antiderivative** of a **difference** of
**function**, just input mathematical expression that contains the difference, specify variable and
apply function antiderivative.

For example, to calculate online an antiderivative of the difference of the following functions `cos(x)-2x` type antiderivative(cos(x)-2x;x), after calculating the result `sin(x)-x^2` is displayed.

**To calculate** **online** an **antiderivative** of **composition of functions** of
the form u(ax+b), where u is a usual function, simply type mathematical expression that contains the function,
specify variable and apply function antiderivative.

For example, to calculate online an antiderivative of the following function `exp(2x+1)` you must enter antiderivative(exp(2x+1);x), after calculating the result `exp(2x+1)/2` is displayed.

For example, to calculate online an antiderivative of the following function `sin(2x+1)` you must enter antiderivative(sin(2x+1);x), to get the following result `-cos(2*x+1)/2`.

For calculation of some functions, calculator is able to use **integration by parts**. The formula used is as follows :
Let f and g be two continuous functions, `int(f'g)=fg-int(fg')`

For example, to calculate an antiderivative `x*sin(x)`, calculator uses the integration by parts, to get the result, you must enter antiderivative(x*sin(x);x), after calculation, result sin(x)-x*cos(x) is returned with steps and detailed calculations.

The antiderivative calculator allows to calculate a primitive online with detail and calculation steps.

This example shows how to use the **antiderivative calculator** to integrate sin (x) + x with respect to x, you must enter:

- antiderivative(sin(x)+x;x) or
- antiderivative(sin(x)+x), when there is no ambiguity about the variable of integration.

See also :

- Antiderivative calculator : antiderivative. The antiderivative calculator allows to calculate a primitive online with detail and calculation steps.
- Derivative calculator : derivative. Derivative calculator allows steps by steps calculation of the derivative of a function with respect to a variable.
- Integral calculator : integral. The integral function calculates online the integral of a function between two values.
- Even or odd function calculator : is_odd_or_even_function. Calculator for determining whether a function is an even function and an odd function.
- Limit of a function : limit. The limit calculator allows the calculation of the limit of a function with the detail and the calculation steps.
- Calculate the Taylor expansion of a function : taylor_series_expansion. The taylor series calculator allows to calculate the Taylor expansion of a function.