How can I evaluate this integral using integration by parts?

In summary, the conversation discusses the use of integration by parts to evaluate the indefinite integral dx/((e^x)(sqrt(1-e(-2x)))) and the confusion over the correct equation to use. After some clarification and guidance, the participant expresses gratitude for the help.
  • #1
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Homework Statement


indefinite integral dx/((e^x)(sqrt(1-e(-2x))))
using integration by parts evaluate the integral.

Homework Equations



integral u*dv = u*v- integral v*du

The Attempt at a Solution



To be completely and entirely honest i am not even sure where to start with this problem. I have finished other integration by parts homework questions in this assignment but this one i can't find something to choose for u and dv that will work out correctly.:grumpy: I have been at this problem alone from almost 2 hours. Any help would be greatly appreciated.
 
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  • #2
Are you sure it wasn't

[tex] \sqrt {1-e^{-2x}} [/tex]

instead of [tex] \sqrt {1-e(-2x)} [/tex], since that is a very strange way of writing it.

If so, just remember that [tex] \frac {1}{e^{x}} = e^{-x} = \sqrt {e^{-2x}} [/tex] and set [tex] u = e^{-2x} [/tex]
 
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  • #3
It was supposed to be
1/ [tex] \sqrt {1-e^{-2x}} [/tex]

**How did you get that equation to show up that way? I just copy and pasted what you had to make it work this time and was curious how i would go about doing that.
 
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  • #4
There is a \frac command in LaTex. To use it just type \frac {numerator}{denominator}

So your problem would show up as:

[tex] \int {\frac{dx}{e^{x}\sqrt{1-e^{-2x}}}[/tex]

**Also check out this guide to LaTex typesetting
https://www.physicsforums.com/misc/howtolatex.pdf
 
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  • #5
Thank You for your help. It is really appreciated.
 
  • #6
If nothing else there is a "^" key on your computer that can be used to indicate exponents.
 

1. What is Integration by Parts?

Integration by Parts is a technique used in calculus to find the integral of a product of two functions. It is based on the product rule for differentiation and involves breaking down a complex integral into simpler integrals that are easier to solve.

2. When should I use Integration by Parts?

Integration by Parts is useful when the integrand (the function being integrated) is a product of two functions that are difficult to integrate separately. It is also useful when the integrand contains a polynomial and an exponential function.

3. What is the formula for Integration by Parts?

The formula for Integration by Parts is ∫u(x)v'(x)dx = u(x)v(x) - ∫v(x)u'(x)dx, where u(x) and v(x) are the two functions being integrated. This formula is derived from the product rule for differentiation.

4. How do I choose u(x) and v'(x) for Integration by Parts?

The choice of u(x) and v'(x) is crucial in Integration by Parts. As a general rule, u(x) should be chosen as the more complicated function in the integrand, while v'(x) should be chosen as the simpler function. This allows for the integral to be simplified by reducing the complexity of one of the functions.

5. Are there any other methods for integration besides Integration by Parts?

Yes, there are several other methods for integration, such as substitution, trigonometric substitution, and partial fractions. These methods are useful for different types of integrals and can often be more efficient than Integration by Parts.

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