Integral involving exponential functions

In summary, for the given integral, \int\frac{1}{c_{1}e^{ax}+c_{2}e^{bx}}dx where a\neq b, there are no detailed references available except for special cases where a = -b or a = 0. The most complete table of integrals, Gradshteyn and Ryzhik, does not have this specific integral, except for certain expressions in the case of definite integrals from 0 to infinity.
  • #1
lequan
6
0
Please help give references on solving the following integral:

[tex] \int\frac{1}{c_{1}e^{ax}+c_{2}e^{bx}}dx [/tex] where [tex] a\neq b [/tex]

Thanks a lot in advance.
 
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  • #2
Gradshteyn and Ryzhik is the most complete table of integrals that I am aware of.
They do not have the integral you want, except for special cases, a = - b or a = 0.
 
  • #3
It seems that we need to get involved in a hypergeometric function, but no more detailed references...
 
  • #4
lequan said:
It seems that we need to get involved in a hypergeometric function, but no more detailed references...
Are you asking for indefinite integral or definite integral? For definite integral [itex](0,\infty)[/itex], the reference I cited above has many expressions that look similar to what you have. As I noted above, nothing for indefinite integral.
 

Related to Integral involving exponential functions

1. What is an integral involving exponential functions?

An integral involving exponential functions is an expression that involves the integration of a function that contains one or more exponential terms. It is a mathematical operation that calculates the area under the curve of a function that contains an exponential term.

2. How is an integral involving exponential functions solved?

An integral involving exponential functions is solved using integration techniques such as substitution, integration by parts, or partial fractions. These techniques help to simplify the expression and make it easier to integrate.

3. What is the importance of integrals involving exponential functions?

Integrals involving exponential functions are important in many areas of science, particularly in physics and engineering. They are used to model real-world phenomena and are essential for solving problems in areas such as thermodynamics, electricity and magnetism, and fluid dynamics.

4. What are some common examples of integrals involving exponential functions?

Some common examples of integrals involving exponential functions include the Gaussian integral, the exponential decay integral, and the Laplace transform. These integrals are frequently used in physics, engineering, and statistics.

5. How can I improve my understanding of integrals involving exponential functions?

To improve your understanding of integrals involving exponential functions, it is important to practice solving different types of integrals and familiarize yourself with the integration techniques used. You can also seek help from a tutor or consult online resources for additional practice problems and explanations.

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