# Integration of an analytical expression

In summary, the analytical equation for equation 3 can be found by integrating equation 2 with respect to x, resulting in a simplified equation using the values of a and b from equation 1.
I have an equation regarding integration equation. Given:

where
is found analytically to be:

My question is what is the analytical equation for equation 3? I hope that anyone may help me regarding this matter. This is the paper I referred: https://arxiv.org/pdf/1503.05793.pdf

Thank you.

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Hello,

Thank you for sharing your question and the paper you referred to. The analytical equation for equation 3 can be found by integrating equation 2 with respect to x. This results in the following equation:

where C is the integration constant. This equation can then be simplified using the values of a and b from equation 1, resulting in the final analytical equation for equation 3:

## 1. What is integration of an analytical expression?

Integration of an analytical expression is a mathematical process that involves finding the antiderivative of a given function. It is the reverse of differentiation and is used to calculate the area under a curve.

## 2. Why is integration of an analytical expression important?

Integration of an analytical expression is important because it allows us to solve complex problems in physics, engineering, and other scientific fields. It also helps us to understand the behavior of a function and make predictions based on its properties.

## 3. What are the different methods of integration?

There are several methods of integration, including substitution, integration by parts, partial fractions, and trigonometric substitution. Each method is used to solve different types of integrals and may be more efficient for certain functions.

## 4. How do you know when to use integration to solve a problem?

Integration is used to solve problems that involve finding the area under a curve or the accumulation of a quantity over a given interval. It is also used to find the antiderivative of a function in order to solve differential equations.

## 5. Can integration of an analytical expression be done by hand or do you need a computer?

Integration of an analytical expression can be done by hand for simple functions using basic integration rules. However, for more complex functions, a computer or calculator is often needed to evaluate the integral numerically.

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