Write out the form of the partial fraction decomposition of the function (as in

Question

Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. (a) x - 6/x^2 + x - 6 A/x - 2 + B/x + 3 (b) x^2/x^2 + x + 6 0 Find integral 7x^3 + 2x/x - 1 dx. Since the degree of the numerator is greater than the degree of the denominator, we first perform the long division. This enables us to write the following. Remember to use absolute values where appropriate.) integral 7x^3 + 2x/x - 1 dx = integral(___________________ + 7x + 9 + 9/___________)dx/- 9ln(|x - 1|)) + 7x^3/3 + 7x^2/2 + 9x + 11/4 + C

Explanation / Answer

x^2/(x^2 +x+6) =1-(x+6)/(x^2 +x+6)

which is of the form

1 + (Ax+B)/(x^2 +x+6)

and that's the required partial decomposition.

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