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Math Help - Completing the Square in Integration

  1. #1
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    Completing the Square in Integration

    When is it necessary to complete the square? What would be an example?
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    Re: Completing the Square in Integration

    becomes very useful in trig substitution problems

    \displaystyle \int \frac{1}{\sqrt{x^2+bx+c}}

    \displaystyle \int \frac{1}{\sqrt{(x+\frac{b}{2})^2+(c-\frac{b^2}{2^2})}}

    use

    \sqrt{(c-\frac{b^2}{2^2})}}\tan \theta = x+\frac{b}{2}
    Last edited by Jonroberts74; July 9th 2014 at 04:13 PM.
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    Re: Completing the Square in Integration

    One thing I'm seeing on You Tube is \int \dfrac{dx}{u^{2} + a} = \dfrac{1}{a}\arctan\dfrac{u}{a} + C

    and you get into this form by completing the square. However, can you be lead in certain situations to other inverse trig functions?
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  4. #4
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    Re: Completing the Square in Integration

    There are a number of integration formulas for
    \int \frac{dx}{x^2+ a}
    \int \frac{dx}{x^2- a}
    \int \frac{dx}{\sqrt{x^2+ a}}
    \int \frac{dx}{a- x^2}
    \int \frac{dx}{x^2- a}, etc.

    All of those can be reached from more complicated integrals by "completing the square".
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