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What trick is used to integrate this?

  1. Jul 20, 2011 #1
    1. The problem statement, all variables and given/known data

    [tex]\int e^x \frac{1 + sin(x)}{1 + cos(x)}\;dx[/tex]

    3. The attempt at a solution

    Apparently there is a trick involving e^x integrals like this

    [tex]\int e^x[f(x) + f'(x)] dx = e^x f(x) + C[/tex]

    Now my question is not how to compute the integral above but where did this [tex]\int e^x[f(x) + f'(x)] dx = e^x f(x) + C[/tex] identity came from?? How does one know this exists?
  2. jcsd
  3. Jul 20, 2011 #2


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    Take the derivative of the result. That may help you see how this works.
  4. Jul 20, 2011 #3
    Yeah, you get this result with integration "by parts", which is the name for using the product rule to rewrite integrals (hopefully in a form you can recognize and solve). If you take a second-semester single-variable calculus class you'll learn about this.
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