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Substitution of u=tan(x/2)

  1. Jun 22, 2010 #1

    I've been doing some additional maths papers and I've seen the use of the substitution u=tan(x/2) in order to calculate integrals. In the mark scheme it states that this particular substitution used to be fairly common, however is not on the modern A-level syllabus.

    Would someone please mind advising me of suitable situations to use such a substitution? I am struggling to see when I should use it.

  2. jcsd
  3. Jun 22, 2010 #2


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    It is useful when your integrand consists of a ratio between to polynomials in of trignometric functions.

    For example:

    Let's look at:

    How would you integrate that one?

    Not very easy, but look at the following:

    Thus, we also have:

    In addition, we have:

    Thus, the above integral can be converted into a rational expression of polynomials in the variable "u", and that can be solved using partial fractions decomposition. :smile:
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