# Indefinite Integral Calculator

The indefinite integral calculator is a beneficial tool for solving indefinite integral problems and solve antiderivative of functions using integral laws.

## Introduction to Indefinite Integral Calculators

An indefinite integral calculator with steps is an online tool that helps to find anti-derivative of a function by using integration laws. This tool helps to evaluate the indefinite integrals. This online indefinite integrals calculator helps its user to solve complicated calculations in calculus.

Integration has two main types:

1. Definite Integrals
2. Indefinite Integrals

Definite integral and Indefinite integrals are almost similar. In calculus, the definite integrals are the exact value/area of the function, which you calculate with definite integral calculator with steps.

On the other hand, the indefinite integral of a function f(x) is a differentiable function of F(x), whose derivative is always equal to the original function f(x). The indefinite integral is also known as primitive integral or antiderivative.

## What is the Notation of Integral Calculator Indefinite?

The indefinite integral calculator uses the same notation of indefinite integrals. To evaluate the indefinite integral, it may be represent as:

$$\int f(x) dx \;=\; F(x)+c$$

Here,
F'(x) = f(x)
c = integral constant

Where C is the added sum in the antiderivative of any function. And the added constant usually indicates the indefinite integral of the function f(x).

## What is Indefinite Integral Calculator with Steps?

In integration, the indefinite integral calculates the integrals without limits or bounded values. It uses the rules and integration techniques to find the problem's solution. The indefinite integral finder use various integration concepts to find accurate results.

But in case if you have limits or bound values of your function with limits, you may try our improper integral calculator with steps.

## How to Use this Calculator Indefinite Integral?

Integration is tricky, but available online tools for calculating indefinite integrals make it relatively more straightforward. By using the following steps, one can quickly get an accurate solution. Ultimately, indefinite integration calculator is one of the problematic problem-solving tools in calculus.

Step 1: Enter the value of Function you want to evaluate.

Step 2: Select the variables from the required field.

Step 3: Click the "CALCULATE" button to get the results.

Step 4: Finally, the antiderivatives of the function will be displayed on the indefinite integrals calculator.

## Basic Formulas Used by Indefinite Integral Calculator

In solving the indefinite integral, the formula used is as follow:

$$\int f(x) dx \;=\; F(x) + C$$

Here f is the original function and F is the derivative of that function f.

The same formula with upper and lower bound values will be used by area under function calculator for exact estimation of area under the graph.

These are some basic indefinite integral formulas that indefinite integral solver uses to evaluate the indefinite integral online. These formulas are:

∫ 1 dx = x + C

∫ a dx = ax + C

∫ xn dx = ((xn+1)/(n+1)) + C; n ≠ 1

∫ sin x dx = - cos x + C

∫ cos x dx = sin x + C

∫ sec2x dx = tan x + C

∫ cosec2x dx = -cot x + C

∫ sec x tan x dx = sec x + C

∫ cosec x cot x dx = -cosec x + C

∫ (1/x) dx = ln |x| + C

∫ ex dx = ex + C

∫ ax dx = (ax/ln a) + C; a > 0, a ≠ 1

For instance, if you find the integral of an integral, you must try double integral solver available in our tools.

Let's see how definite integral formulas utilize above formulas for solving integrals with a stepwise solution. Let's put an eye on the manual example problem

### Evaluate the Indefinite Integral Calculator : (an Example)

Simplify the given indefinite integral problem: ∫ 2x5 -12x2 + 9 dx

Solution:

$$\int (2x^5 - 12x^2 + 9) dx$$

Now Integrate the given indefinite integral function, and it becomes:

$$\int (2x^5 - 12x^2 + 9) dx \;=\; 2 (\frac{x^6}{6}) - 12 (\frac{x^3}{3}) + 9x + C$$

Here point to be noted as not to forget the integration constant "C".

And after the simplification, the solution we get is,

$$\int (2x^5 - 12x^2 + 9) dx \;=\; \frac{x^6}{3} - 4x^3 + 9x + C$$

The same results with step b step solution will obtain by using indefinite integration calculator.

Related: Also try our 3d integral calculator for the calculation of integrand thrice on a single click.

## Benefits of Using Indefinite Integrals Calculator

Whenever you solve your calculus problems, a door of errors opens to you. By using a calculator indefinite integral in solving calculus problems, one can enjoy the following benefits:

• Accuracy
• Release stress
• Convenient in use
• Faster execution
• Reliable results
• Labor-saving ˗ the user doesn't need to do extensive calculations manually.

Hopefully, this indefinite integral solver will be helpful for your complex math calculation. So stay tunned with integral solver website for better and efficient learning.

## Frequently Asked Question

### What does an indefinite integral show?

As the indefinite integrals are the function of any f derivative so it shows us the family of derivatives of any function.

So our indefinite integral finder made it easy to do calculations with the family of derivatives in a seconds.

### What is the Indefinite Integral of ln x

To find the indefinite integral of ln x concerning x the integration by parts can be used which is mathematically written as,

$$\int u\;dv \;=\; uv - \int v\; du$$

Use the integration by parts,

$$\int ln\;x\;dx \;=\; x\;ln\;x - \int \;x . \frac{1}{x} \;=\; x\;ln\;x - \int dx \;=\; x\;ln\;x - x + C$$

Therefore, the definite integral of ln x is,

$$\int ln\;x\;dx \;=\; x\;ln\;x - x + C$$

### What is the Indefinite Integral of 3x/x+5

To solve indefinite integral online of 3x/x+5 rewrite the integrand and use the simple integration techniques,

$$3 . \frac{x}{x+5}$$

Rewrite x in terms of x+5,

$$x \;=\;\; (x + 5) - \;5$$

Thus the integrand is,

$$3 . \frac{x}{x+5} \;=\; 3 . \frac{(x+5)- 5}{x + 5} \;=\; 3 . \biggr(1 - \frac{5}{x + 5} \biggr)$$

So the integral becomes,

$$\int \frac{3x}{x+5} dx \;=\; 3 \int 1\; dx - 3 \int \frac{5}{x+5} dx$$

The integral of the constant is,

$$3 \int 1 \;dx \;=\; 3x$$

$$-3 \int\; \frac{5}{x +5} dx \;=\; -15 \;ln(x+5)$$

$$\int \frac{3x}{x+5} dx \;=\; 3x - 15 ln(x + 5) + C$$

### What is the Indefinite Integral of arcsin u

To evaluate indefinite integral of arcsin u use the integration by parts method, and the formula is given below

$$\int u\;dv \;=\; uv - \int v\;du$$

Applying the formula,

$$\int arcsin(u) du \;=\; u arcsin(u) - \int u . \frac{1}{\sqrt{1-u^2}} du$$

$$\int \frac{u}{\sqrt{1 - u^2}} du \;=\; - \sqrt{1 - u^2}$$

Returning to integration by parts results,

$$\int arcsin(u) du \;=\; uarcsin(u) + \sqrt{1 - u^2} + C$$

### Are there any limits or bounds present in the indefinite integrals?

No, there are no limits and bounds present in the indefinite integrals.

### What is the integral of 0?

In calculus, the derivative of any constant (number or value) is zero. And integration is the opposite of differentiation. So, in this case, the value for the 0 is C constant.

Therefore, ∫0 dx = C.