# Indefinite Integral Calculator

This indefinite integral calculator is a free online tool to evaluate the antiderivative of a function. We know that integral calculation is a tedious process with a variety of functions to remember and procedures to do. This free online calculator can make it really fast and easy. Try it out!!

## Using the Integral Calculator

1. Enter the function to integrate into the first column.
2. Enter the variable with respect to which the integral has to be calculated in the second column.
3. Click the Submit button.
4. The antiderivative of the function will be displayed and related graphs will also be displayed.

## Integration

### What is Integration?

Integration is one of the two main operations of calculus; its inverse operation, differentiation, is the other. An integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Basically, integration is the same as anti-differentiation or is the reverse process of differentiation. (Fundamental Theorem of Integration)

There are two types of integrals namely definite and indefinite integrals.

Definite Integrals: Calculating definite integral consists of a lower and upper bound and we get a number as a result which is basically the area bounded by the graph, lower and upper bounds and the coordinate axes.
Indefinite Integrals: Calculating indefinite integrals basically gives us the antiderivative of the function. Differentiating the result will give you the initial function again.

Related: Definite Integral Properties

### Frequently Used Indefinite Integrals

#### General and Logarithmic Integrals

1. ∫ adx = ax + C
2. ∫ exdx = ex + C
3. ∫ axdx = (ax/ lna) + C
4. ∫ 1/x dx = ln|x| + C
5. ∫ xndx = (xn+1/n+1) + C, when n ≠ −1

#### Trigonometric Integrals

1. ∫ cos(x) dx = sin(x) + C
2. ∫ sec2(x) dx = tan(x)+C
3. ∫ sin(x) dx = − cos(x) + C
4. ∫ csc2(x) dx = − cot(x) + C
5. ∫ sec(x) tan(x) dx = sec(x) + C
6. ∫ 1/(1+x2) dx = arctan(x) + C
7. ∫ 1/(√1−x2) dx = arcsin(x) + C
8. ∫ csc(x) cot(x) dx = −csc(x) + C
9. ∫ sec(x) dx = ln|sec(x) + tan(x)|+C
10. ∫ csc(x) dx = ln|csc(x) − cot(x)| + C

Hope, the calculator helped you in solving integrals!

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