Integration of an exponential and algebra

In summary, the conversation is about a question involving an integral with a complicated expression inside the integrand. The person tried using substitution but was unable to solve it. They suggest getting rid of the term ex but are unsure how to do so. Another person suggests trying online resources like Wolframalpha or Symbolab, but the results were not helpful. The conversation also includes a discussion about the practical range of x values and whether having bounds of integration could help solve the problem.
  • #1
songoku
2,366
347
Homework Statement
Please see below
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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  • #2
Have you tried Wolframalpha or Symbolab.com ?

Looking at the expression inside the integrand, what would be a practical range of x values?
 
  • #3
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
 
  • #4
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.
 

FAQ: Integration of an exponential and algebra

What is the formula for integrating an exponential function?

The formula for integrating an exponential function is ∫e^x dx = e^x + C, where C is the constant of integration.

How can I integrate an exponential function with a variable in the exponent?

To integrate an exponential function with a variable in the exponent, you can use the substitution method. Let u = the variable in the exponent, then substitute u and du into the integral and solve for the new integral in terms of u.

Can I use algebraic manipulation to integrate an exponential function?

Yes, you can use algebraic manipulation to integrate an exponential function. You can use properties of logarithms and exponents to simplify the integral and make it easier to solve.

What is the benefit of integrating an exponential function using algebraic methods?

The benefit of integrating an exponential function using algebraic methods is that it allows for a more efficient and accurate solution. It also helps to understand the relationship between the exponential and logarithmic functions.

Are there any special cases when integrating an exponential function?

Yes, there are special cases when integrating an exponential function. One special case is when the exponent is a negative number. In this case, you can use the power rule for integration to solve the integral.

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