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Math Help - [SOLVED] Integration using tan 1/2x substitution

  1. #1
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    Question [SOLVED] Integration using tan 1/2x substitution

    Im struggling to finish this one

    I = 1/( 2 + cos x) dx

    using substitution t = tan1/2 x

    I sub in for cos and recalcualte to give me

    I = 2/(t^2 + 3) dt

    I can see this is clse tot the form I = a/(t^2 + a^2) dt but can complete.

    Can someone show me where I'm missing the link?

    Thanks, Dan
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  2. #2
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    Quote Originally Posted by dojo View Post
    Im struggling to finish this one

    I = 1/( 2 + cos x) dx

    using substitution t = tan1/2 x

    I sub in for cos and recalcualte to give me

    I = 2/(t^2 + 3) dt

    I can see this is clse tot the form I = a/(t^2 + a^2) dt but can complete.

    Can someone show me where I'm missing the link?

    Thanks, Dan
    Dear Dan,

    \int{\frac{2}{3+t^2}}dt=2\int{\frac{dt}{(\sqrt{3})  ^2+t^2}}

    You may recall that, \frac{1}{a}tan^{-1}\frac{t}{a}=\int{\frac{dt}{a^2+t^2}}

    Hope this will help you to solve the problem.
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