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Math Help - Integrals

  1. #1
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    Integrals

    1. Evaluate K=integral((x+4)^2/(x^2+8x+17)^(5/2))dx. The lower limit is -4 and the upper limit is -3.

    I have first tried by completing the square of the bottom polynomial which gives (x+4)^2+1 and i know I am supposed to use partial fraction decomposition. The thing that troubles me with this question is splitting it up so i can work from a common denominator and find the coefficients. Help is much apppreciated!

    2. Evaluate J=integral((7x^2+42x+72)/((x+3)^2(x^2+6x+18)))dx.

    I started of this question by using the substitution u=x+3, but im not entirely sure what to do to decompose into partial fractions.

    Thanks to all who helped.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    For 1 use the trig substitution x+4 = tan(t)


    For 2 use a partial fraction decomp
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  3. #3
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    I know that, but i cant fiqure it out still.
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  4. #4
    MHF Contributor Calculus26's Avatar
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    See attachment
    Attached Thumbnails Attached Thumbnails Integrals-integral1.jpg  
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