## Introduction to U Substitution Calculator

U sub calculator is a free mathematical tool that is used to find the solution of complex integral questions.

Integral substitution calculator determines the integral function who do not solve by any other method of integration in the run of time.

the u-substitution method is used to simplify integrals by substituting a part of the integrand with a new variable, usually denoted as u. This substitution allows for the integral to be rewritten in terms of the new variable, potentially making it easier to evaluate.

Additionally, Our calculator automates this process, providing solutions to integrals using the u-substitution method. It's particularly useful for integrals where the derivative of a function within the integrand is also present. Further, if you would like to find the antiderivative for the given function, you can utilize our integration by part calculator. Our Calculator also serves as a valuable tool for solving integration problems efficiently and accurately, empowering users to tackle complex mathematical challenges with confidence.

## What is U Substitution?

U substitution is a technique that is used to calculate the complicated integral function with the substitution of u from the original function of the integrand to easily integrate the function.

The basic idea behind u-substitution is to identify a function u (referred to as the "substitution function") and its derivative du such that the integral can be expressed in terms of u. This substitution allows for the integral to be rewritten in a form that is easier to evaluate.

U-substitution is particularly useful for integrals involving compositions of functions, such as trigonometric, exponential, or logarithmic functions, as well as algebraic expressions. Additionally, if you would like to find integral problems of rational algebraic expression, you can use our partial fraction solver. Our calculator also evaluates the antiderivative function where the degree of the numerator is higher than the degree of the denominator expression.

## Formula Used by Integration by Substitution Calculator

U substitution formula has a function of f in g(x). Our U substitution calculator with steps use the following formula for calculations,

$$ \int f(g(x)) g’(x)dx \;=\; \int f(u) du \;=\; F(u) + C $$

Where,

g(x): function,

g`(x): derivative of g(x).

f(g(x)): replace with u as f(u)

g`(x)dx: du.

F(u): shows integration solution in terms of u

C: integration constant for indefinite integral function

## Working Method of U Sub Calculator

The u substitution method is used to replace the original terms of integrand with another term u and dx as du to manipulate the given expression so that it can be integrated easily. This method is used when no other method of integration gives the solution of the complicated integral problem.

When you give input in the substitution integral calculator, it will identify the nature of the function if a function and its derivative both are present in a given problem like g( f(x)f`(x)) as an integrand or not. If g is continuous at the range of f(x) then the u-substitution rule of integration applies.

In the u substitution rule, some part of the integrand function f(x) is considered as u and after taking the derivative of u as du, usub calculator considered it as du=f`(x)dx.

After that u-substitution calculator integrate the function and solution gets in terms of u. Then replace the u term from the original function f(x) to get the solution according to the given integrand form.

In the case of definite integral, the integration by substitution calculator apply upper and lower limit first and then replace u with original function. For further clarification, you can utilize the limits of integration calculator to solve definite integrals with specified limits, providing a comprehensive approach to integral calculus problems. Now let's see an example of U substitution to get clarity on this concept.

## Example of U Substitution Method

The u substitution calculator with steps is used to solve the u substitution problems and it will help you solve it but you also have to know the manual calculations. Here’s an example of manual calculation.

### Example:

Evaluate the integral:

$$ \int \frac{sin t}{cos^3 t} dt $$

**Solution:**

The derivative of cos t is -sint, so we set u=cost. du= -sint dt.

$$ \int \frac{sint}{cos^3 t} dt \;=\; -\int \frac{du}{u^3} $$

Evaluating the integral,

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

Put the answer back,

$$ \int \frac{sint}{cos^3 t} dt \;=\; \frac{1}{2u^2} + C \;=\; \frac{1}{2cos^2 t} + C $$

Thus it is the final solution of our function with specific limits. If you would like to explore further solutions or perform additional computations based on this result, you can use the calculate integral with steps. This tool allows for the integration of various functions and offers additional functionalities for advanced mathematical analysis.

## How to Use U Substitution Calculator?

Integration by substitution calculator is a user-friendly interface so that you can use it to solve complicated integral problems if you follow some simple steps. These steps are:

- Enter your integral function(definite or indefinite) in the input field
- Select a variable from the given list through which you want to evaluate integral
- If the function is definite integral then add the upper and lower limits in the respective field
- If a function is indefinite then you do not need to add limit values for the result
- Press the “Calculate” button to get the solution of the integral problem in the u sub calculator.

## Result Obtained from Integral Substitution Calculator

After giving the input value in the u-substitution calculator, you will obtain the solution of the given integral question instantly. It may contain as:

For more comprehensive calculations, you can also utilize our solve indefinite integral to further analyze related integrals and mathematical expressions. Our calculator also offers a range of functionalities for exploring indefinite integrals in depth, allowing for a deeper understanding of mathematical concepts and techniques.

- Result section provides a solution of the integral problem
- Possible steps section gives solutions with steps for more clarity
- Plot section makes a graph according to the result calculation of the given integral problem

## Advantages of Substitution Integral Calculator

U substitution calculator with steps provides you tons of benefits when you use it for the calculation of complex integral problems. These benefits are:

If you're interested in exploring more mathematical tools and calculators for various applications. Further, if you're interested in exploring more mathematical tools and calculators for various applications, you can access our comprehensive collection of calculators by visiting the All Calculators page.

- It saves time and effort in doing complex calculations of integral problems
- It provides accurate results of given integral while using our calculator.
- It provides you with a speedy solution of the integral function
- It has a simple design, anyone can use it easily.
- You can use it for unlimited calculation of u-substitution integral problems

## Conclusion

This usub calculator is the most beneficial tool as it provides a solution of the complex integral using the u-substitution method. You do not need to do lengthy calculations while calculating these types of integral questions in no time.

U substitution calculator is a trustworthy tool because it is certified or tested by world-famous university professors or mathematicians.

You can explore more calculators like trig sub calculator for more evaluation of integral problems.