Solving an Integral: x^(0.5)*exp(x)dx

  • Thread starter smadar ha
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    Integral
In summary, the conversation is discussing how to solve the integral x^(0.5)*exp(x)dx. Suggestions were given to use integration by parts and substitution, but it was mentioned that the integral may not be able to be solved using elementary functions. It was also suggested to swap variables in the second integration by parts step.
  • #1
smadar ha
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How can I solve the following integral:

x^(0.5)*exp(x)dx

Thanks.
 
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  • #2
use integration by parts
 
  • #3
I tried but it gives me another integral that I can't solve:

x^(-0.5)*exp(x)dx
 
  • #4
smadar ha said:
I tried but it gives me another integral that I can't solve:

x^(-0.5)*exp(x)dx
Now use integration by parts again, but this time swap your variables around so that you are integrating x-0.5 and differentiating ex.
 
  • #5
if I do it I recieve:

integral(x^0.5*exp(x))=integral(x^0.5*exp(x))

and it doesn't help me...
 
  • #6
smadar ha said:
if I do it I recieve:

integral(x^0.5*exp(x))=integral(x^0.5*exp(x))

and it doesn't help me...
Indeed it doesn't. In that case I would suggest I substitution of the form u=x0.5, followed by integration by parts. However, I will point out at this point that the integral probably cannot be written in terms of elementary functions and you will most likely have to make use of the error function.
 
  • #7
I think that may help.

Thanks a lot.

Smadar.
 
  • #8
no you can actually solve this problem by integration by parts, just do wat hootenanny said you will have to integrate by parts twice but you would have to swap the variables in the second case...
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is used to calculate the total value of a function over a specific interval.

2. What is the purpose of using an integral?

The main purpose of using an integral is to calculate the total value of a function over a given interval. It is also used in various applications such as finding the area of a shape, calculating displacement in physics, and determining the probability of an event in statistics.

3. How is an integral calculated?

An integral is calculated using a process called integration, which involves finding the antiderivative of a function and evaluating it at the upper and lower limits of the given interval. This process can be done analytically or numerically using various techniques such as the fundamental theorem of calculus, substitution, and integration by parts.

4. What is the difference between definite and indefinite integrals?

A definite integral has specific limits of integration, while an indefinite integral does not. This means that a definite integral will give a numerical value, while an indefinite integral will give a function as the result. Additionally, a definite integral is used to calculate the area under a curve, while an indefinite integral is used to find the original function when its derivative is given.

5. What are some real-world applications of integrals?

Integrals are used in various fields, such as physics, engineering, economics, and statistics. Some examples of real-world applications include calculating the work done by a force, determining the volume of a solid, finding the center of mass of an object, and calculating the expected value of a random variable.

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