Heklp with an integral involving the exp function

In summary, the conversation discussed a difficult integration problem involving exponential functions and a variable transformation. The integrals in question were divergent at 0 and may be expressed in terms of the non-elementary exponential integral function.
  • #1
xnr
1
0
Hi everyone

I've been dealing with a rather difficult (at least for me) integration problem which I am not able to find in integration tables I've been consulting.
After a variable transformation I ended up with the following sets of integrals:

[tex]\\int[/tex] e[tex]^{y}[/tex]/y[tex]^{2}[/tex]dy from 0 to t (t is not infinity) and

[tex]\\int[/tex] e[tex]^{y}[/tex]/y[tex]^{3}[/tex]dy also from 0 to t and

(sorry I could not get the integral symbol to work, so I used int instead)

thanks
xnr
 
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  • #2
Neither of those looks convergent (at 0) to me.
 
  • #3
As Halls said, they diverge at 0. The indefinite integral of exp(y)/y is a non-elementary function known as the "exponential integral" function. Your two integrals may be expressed in terms of the exponential integral function using integration by parts.
 

FAQ: Heklp with an integral involving the exp function

What is the exp function?

The exp function, also known as the exponential function, is a mathematical function that is commonly used to model growth or decay in many natural and physical phenomena. It is defined as e^x, where e is the mathematical constant approximately equal to 2.71828 and x is the exponent.

How is the exp function related to integrals?

The exp function is closely related to integrals as it is often used in the integration of exponential functions. In particular, the integral of the exp function is equal to itself, making it a very useful function in solving integrals involving exponential terms.

Can you provide an example of an integral involving the exp function?

One example of an integral involving the exp function is ∫e^x dx, which evaluates to e^x + C, where C is the constant of integration. This integral can also be written as ∫e^x x^r dx, where r is any real number, and its solution is also e^x + C.

What are some common techniques for solving integrals involving the exp function?

Some common techniques for solving integrals involving the exp function include using integration by parts, substitution, and partial fractions. It is also helpful to be familiar with the properties of the exp function, such as its derivative being equal to itself.

Are there any special cases or exceptions when integrating with the exp function?

Yes, there are some special cases or exceptions when integrating with the exp function. For instance, if the integral involves a complex exponent, the solution may involve complex numbers. Additionally, when integrating with limits, the exp function may have to be evaluated at the boundaries of the interval. It is important to carefully consider these cases when solving integrals involving the exp function.

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