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Math Help - Reduction formula problem..

  1. #1
    Junior Member
    Joined
    Feb 2010
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    37

    Lightbulb Reduction formula problem..

    Can someone help me with this question..

    For the integral \int{\frac{1}{( x^2 + 1 )^n}} dx prove the reduction formula :
    I_{n} = \frac{1}{n-2} . \frac{x}{(x^2+1)^{n-1}} + \frac{2n - 3}{2n-2}I_{n-1}


    Thanks
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  2. #2
    Junior Member
    Joined
    Feb 2010
    Posts
    37

    Talking Re: Reduction formula problem..

    How to find the integral of
    a) \int{\frac{3}{\sqrt{6 + 4x - x^2}}}

    and

    b) \int{\frac{3x^2}{\sqrt{x^2 - 9}}}

    for b) The answer in the ans sheet is this

    \frac{3x \sqrt{x^2 - 9}}{2} + \frac{27}{2} ln (x + \sqrt{x^2 -9}) + C

    What I've found is this :

    \frac{27}{3} ln (\frac{1}{3} + \sqrt{x^2 -9})

    and

    c) \int{x^3 ln (ax)}

    Ans : -\frac{x^4}{10}+ \frac{x^4 ln (ax)}{4}

    My ans : -\frac{x^4}{16}+ \frac{x^4 ln (ax)}{4}
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