## Introduction to U Substitution Calculator:

U Substitution Calculator with steps is an online tool that helps you evaluate indefinite integral and definite integral problems. Our tool determines the complex structure of integral function into a simplified form to make the integration process easy.

The integration by substitution calculator is a helpful tool for everyone who want to **solve** the complicated form of an integral function without doing complex calculations. Our tool simplifies the given integral function with the help of the u-substitution method.

## What is U Substitution?

U substitution is a process that is used to convert the complex structure of a given integral function into simple form to make the **integration process** smooth and easy. After evaluating the integral replace the u value with its original function value.

You can use this method to get a solution of both types of integrals, definite or indefinite integral. The notation that the u sub calculator uses to express u-substitution is given as,

$$ \int f[g(x)] g’(x) dx \;=\; \int f(u) du $$

Where g(x) is the integral function and g`(x) is the derivative of the given function f(u) which is the supposed value and du is replaced by dx when you differentiate it with respect to u. The integration solution we get is,

$$ =\; F(u) + C $$

$$ =\; F(g(x)) + C $$

## How to Do U Substitution?

U substitution method can make the integration process easy and you get the solution of the integral function without any difficult method for integration. Let us see how the u substitution calculator with steps **calculates the integral** problems with the help of an example. The stepwise calculation for u substitution is:

### Example: Find the integral

$$ \int z \sqrt{z^2 - 5} dz $$

**Solution**:

**Step1**:

As you can see the given function has a complex form so the integral substitution calculator uses the u-substitution method.

**Step2**:

For that suppose the given values in the function are equal to u and du form,

$$ u \;=\; z^2 - 5 $$

$$ du \;=\; 2zdz $$

$$ \frac{1}{2} du \;=\; \frac{1}{2}(2z) dz \;=\; z\; dz $$

**Step3**:

Put these values in the given function,

$$ \int z(z^2 - 5)^{\frac{1}{2}} dz \;=\; \frac{1}{2} \int u^{\frac{1}{2}} du $$

**Step4**:

Evaluate the integral of the above function. As you can see the above integral function becomes the simplest function of integration after using the u-substitution method. Apply the power rule of integration such as,

$$ \frac{1}{2} \int u^{\frac{1}{2}} du \;=\; \left( \frac{1}{2} \right) \frac{u^{\frac{3}{2}}}{3} + C $$

$$ =\; \left( \frac{1}{2} \right) \left(\frac{2}{3} \right) u^{\frac{3}{2}} + C $$

$$ =\; \frac{1}{3} u^{\frac{3}{2}} + C $$

**Step 5**:

Now replace u with the given original function value for the solution.

$$ =\; \frac{1}{3} (z^2 - 5)^{\frac{3}{2}} + C $$

**Step 6**:

If the given function is a definite integral function then the u-substitution method is the same but after integration, you can apply the limits to get a solution.

The usub calculator do this all procedure and gives an updated answer which solves your all queries about the question.

## How to Use the U Substitution Calculator?

The integration by substitution calculator has a user-friendly design that allows you to give different types of integration functions to get solutions immediately.

You just need to put your input function in this u sub calculator by following some simple steps that help you to get results without any inconvenience. These steps are:

- Enter the integral function that you want to evaluate for u-substitution in the input field.
**Add the variable**of integration.- If the function is a definite integral function then add the upper and lower limit values in the input field.
- Review your given input value before clicking the calculate button to get the solution of the integral function.
- Click the “Calculate” button of integral substitution calculator for the solution of integral problems.
- If you want to check the how the substitution integral calculator works then use the load example for the calculation of integral.
- Click the “Recalculate” button for the evaluation of more questions of the u-substitution integral problem.

## Results from Integration by Substitution Calculator:

U substitution calculator with steps provides you with a solution of u-substitution problem as per your input. It provides solution in different form which includes:

**Result Box:**

When you click on the result button you get the **solution** of the u-substitution integral problem.

**Steps Box:**

Click on the steps option so that you get the step by step solution of your u substitution integral questions.

## Benefits of Using U Sub Calculator:

The usub calculator has **multiple benefits** that you can avail whenever you use it to get a solution of u-substitution integration problems. These benefits are:

- Our u-substitution calculator only takes the input value of the integral function and gives a solution without imposing a condition of a sign-up option.
- It is an unlimited tool which means you can use it as many times as you can for calculations.
- The integration by substitution calculator is a trustworthy tool as it always provides you with accurate solutions for the substitution of integral problem.
- It is a speedy tool that evaluates the integral problems with the help of u-substitution method and gives solutions in a couple of seconds.
- The integral substitution calculator is a learning tool that helps children to learn the concept of integral function very easily without going to any teacher.
- The substitution integral calculator is a free tool that allows you to use it for the calculation of u-substitution integration problems without spending a single penny.
- It is an easy-to-use tool, anyone even a beginner can easily use it for the solution of integral problems of the u-substitution method.
- U substitution calculator with steps can operate on a desktop, mobile, or laptop through the internet to solve integral-function problems.