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Math Help - Solve The Following Trigonometric Integral. (3)

  1. #1
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    Solve The Following Trigonometric Integral. (3)

    Hello
    here is it:
    \int ( cos(x) + 1 )^{\frac{3}{2}} dx
    I used u=cos(x)+1
    Then, I got :
    - \int \frac{u^{\frac{3}{2}} }{ \sqrt{ 1 - (u-1)^2 }} du
    Using the trigonometric substitution u-1=sin(\theta), I got:
    - \int (sin(\theta) + 1)^{\frac{3}{2}} du

    I think I will do the same work again and I will get the original integral in another variable.
    then I will moved it the left hand side.
    Since \int f(x) dx = \int f(u) du = \int f(\theta) d\theta ....
    And I will devide by the resulting coefficient.
    I think you understood what I mean.
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Santiago, Chile
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    Hint: \cos x=2\cos ^{2}\frac{x}{2}-1.
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