# Integral Calculator



A step by step indefinite integral calculator of functions is presented.

## Definition of Indefinite Integral

The indefinite integral $\displaystyle \int f(x) dx$ of function $f(x)$ is given by $\displaystyle \int f(x) dx = F(x) + C$ such that $F'(x) = f(x)$.
$C$ is the constant of integration and $F(x)$ is called the antiderivative.
Note that once the indefinite integral of $f(x)$ is calculated, one way to check your answer is to find $F'(x)$ and compare it to $f(x)$

Example
$\displaystyle \int (x^2 + 1) dx = \dfrac{1}{3} x^3 + x + C$ , hence $F(x) = \dfrac{1}{3} x^3 + x$ because $F'(x) = \dfrac{1}{3} (3x^{3-1} )+1 = x^2 + x$

## Use of the Indefinite Integral Calculator

1 - Enter and edit function $f(x)$ and click "Enter Function" then check what you have entered.
Note that the five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: f(x) = x^3 - 2*x + 3*cos(3x-3) + e^(-4*x)).(more notes on editing functions are located below)
2 - Click "Calculate Integral" to obain the antiderivative $\displaystyle F(x)$.

$f(x)$ =

Notes: In editing functions, use the following:
1 - The inverse trigonometric functions are entered as:     arcsin()     arccos()     arctan() and the inverse hyperbolic functions are entered as:     arcsinh()     arccosh()     arctanh()
2 - The five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: f(x) = 2*x^3 + 3*cos(2x - 5) + ln(x))
3 - The function square root function is written as (sqrt). (example: sqrt(x^2-1)
4 - The exponential function is written as (e^x). (Example: e^(2*x+2) )
5 - The log base e function is written as ln(x). (Example: ln(2*x-2) )
Here are some examples of functions that you may copy and paste to practice:
x^2 + 2x - 3       (x^2+2x-1)/(x-1)       1/(x-2)       ln(2*x - 2)      sqrt(x^2-1)
2*sin(2x-2)       e^(2x-3)       1/sqrt(x^2-1)       1/sqrt(1-x^2)