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  • 5 years ago

what is the partial decomposition of... x^3+x^2-5/(x^2+7)^2

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  1. anonymous
    • 5 years ago
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    so the denominator is a square of an irreducible quadratic, so it has to separate to (Ax+B)/(x^2+7) + (Cx+D)/(x^2+7)^2. Then you have to multiply by the denominators to get what you are looking for, so \[x^3+x^2-5=(Ax+B)(x^2+7)+(Cx+D)\]\[x^3+x^2-5=x^3(A)+x^2(B)+x(7A+C)+(7B+D)\ so A=1, B=1, -7 = C and -12=D. by relating the coefficients on the left to the ones on the right. Then sub in your values andyou have your decomposition. and can integrate.

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