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. ∫* e ^{x}dx* =

*e*+

^{x}*C*

3. ∫

*a*= (

^{x}dx*a*ln

^{x}/*a)*+

*C*

4. ∫ 1/

*x dx*= ln|

*x*| +

*C*

5. ∫

*x*=

^{n}dx*(x*/

^{n+1}*n*+1) +

*C*,

*when n*≠ −1

**Trigonometric Integrals**

1. ∫ cos(*x) dx* = sin*(x*) +* C*

2. ∫ sec^{2}(*x) dx* = tan(*x)*+*C*

3. ∫ sin*(x) dx* = − cos*(x)* + *C*

4. ∫ csc^{2}(*x) dx* = − cot(*x)* + *C*

5. ∫ sec*(x*) tan*(x) dx* = sec*(x*) +* C*

6. ∫ 1/(1+*x*^{2}) *dx* = arctan*(x*) +* C*

7. ∫ 1/(√1−*x*^{2}) *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!