Integration of an exponential and algebra

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Homework Help Overview

The discussion revolves around the integration of a complex expression involving an exponential function and algebraic terms. The original poster attempts to solve the integral of the form \(\int \frac{e^x (2-x^2)}{(1-x) \sqrt{1-x^2}} dx\) using substitution but encounters difficulties.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of substitution and question the solvability of the integral, noting attempts to use online tools like Wolframalpha and Symbolab. They also explore the implications of the function's domain on the integration process.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some suggest that the presence of bounds might influence the ability to find a solution, while others express uncertainty about the integral's solvability.

Contextual Notes

There is mention of the domain of the function being defined as -1 < x < 1, which raises questions about its relevance to solving the integral.

songoku
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Homework Statement
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Relevant Equations
integration
##\int \frac{e^x (2-x^2)}{(1-x) \sqrt{1-x^2}} dx##

I tried using substitution x = sin θ but still can not solve it. I guess I have to get rid the term ex but do not know how

Thanks
 
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Have you tried Wolframalpha or Symbolab.com ?

Looking at the expression inside the integrand, what would be a practical range of x values?
 
Sorry for late reply.

scottdave said:
Have you tried Wolframalpha or Symbolab.com ?
Wolframalpha wrote not result found in terms of standard mathematical functions and symbolab wrote no steps: steps are currently not supported for this problem (but not result given)

So this means that the question is not solvable?

Looking at the expression inside the integrand, what would be a practical range of x values?
The domain where the function is defined will be -1 < x < 1. Is this what you mean? I do not understand what the domain has to do with solving the integral.

Thanks
 
I think he means whether there was bounds of integration, if it was a definite integral perhaps there could be a solution you could manage.
 

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