Integral of dx/Sqrt[exp(-x)+x+c]

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In summary, the integral of dx/Sqrt[exp(-x)+x+c] is a mathematical representation of the area under the curve of the function dx/Sqrt[exp(-x)+x+c]. It can be solved using various methods such as integration by parts, substitution, or using a table of integrals. The constant "c" represents the arbitrary constant of integration and is important to include in the solution. It can be evaluated using a calculator, but may not provide a solution for symbolic integration. Real-world applications include physics, economics, engineering, and statistics.
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nassboy
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Does anybody know if it is possible to find the anti-derivative of 1/Sqrt[exp(-x)+x+c] with respect to x. Mathematica was unable to compute it. Would it be possible to convert it into a form where residue theory is applicable?
 
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  • #2
Residue theory is usually only good for computing infinite integrals, or integrals from 0 to 2pi. I'm not aware of any way to compute a general anti-derivative using it
 
  • #3
What if I made it a definite integral...and integrated from xa to xb.
 
  • #4
and then apply some sort of conformal mapping to change it to an infinite integral
 

1. What is the meaning of the integral of dx/Sqrt[exp(-x)+x+c]?

The integral of dx/Sqrt[exp(-x)+x+c] is a mathematical representation of the area under the curve of the function dx/Sqrt[exp(-x)+x+c]. It is often used in calculus to solve problems related to finding the area of a curve or the total change in a quantity over time.

2. How do you solve the integral of dx/Sqrt[exp(-x)+x+c]?

To solve the integral of dx/Sqrt[exp(-x)+x+c], you can use a variety of methods such as integration by parts, substitution, or using a table of integrals. It is important to carefully choose the appropriate method for each specific problem in order to find an accurate solution.

3. What is the significance of the constant "c" in the integral of dx/Sqrt[exp(-x)+x+c]?

The constant "c" in the integral of dx/Sqrt[exp(-x)+x+c] represents the arbitrary constant of integration. This constant is added to the solution of the integral to account for any unknown information that may affect the overall value. It is important to include this constant in the solution to accurately represent the original function.

4. Can the integral of dx/Sqrt[exp(-x)+x+c] be evaluated using a calculator?

Yes, the integral of dx/Sqrt[exp(-x)+x+c] can be evaluated using a calculator if the function is integrated numerically. However, if the integral is solved symbolically, the calculator may not be able to provide a solution due to the complexity of the problem.

5. What are some real-world applications of the integral of dx/Sqrt[exp(-x)+x+c]?

The integral of dx/Sqrt[exp(-x)+x+c] has many real-world applications, such as in physics to calculate the work done by a varying force, in economics to find the total cost or profit over time, and in engineering to determine the displacement of a system. It is also commonly used in statistics to find the total probability of an event occurring within a certain range.

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