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Integral help

  1. Sep 10, 2005 #1
    I was wondering what the best way to do this integral was:

    Integral of 1+sin(x) all over cos(x)^2

    Is subsitution the best way?
  2. jcsd
  3. Sep 10, 2005 #2
    The easiest way is to write the fraction as the sum of fractions ((a+b)/c = a/c + b/c)) and integrate the first and second terms of the sum separately. One is a basic antiderivative and the other is a simple substitution.
  4. Sep 10, 2005 #3


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    Homework Helper

    So what hypermorphism means is that you do:

    [tex]\int {\frac{{1 + \sin x}}{{\cos ^2 x}}} dx = \int {\frac{1}{{\cos ^2 x}}} dx + \int {\frac{{\sin x}}{{\cos ^2 x}}} dx[/tex]

    As he said, the first one is a standard antiderivative, for the second one try [itex]y = \cos x[/itex]
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