11. Decompose the following functions into its partial fraction a) \frac{17x-53}{x^2-2x-15} b) \frac{3x^2}{x^2+1} c) \frac{4x^3+16x^2+23x+13}{(x+1)^3(x+2)} d) \frac{x^5}{x^4-1}
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Step 1: For function a) -2x-15, we cannot decompose it into partial fractions because it is a linear function and does not have any denominators. Show more…
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In the partial fraction decomposition
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A The form of the partial fraction decomposition of a rational function is given below. (15x-7x^2-8)/((x-3)(x^2+4)) = A/(x-3) + (Bx+C)/(x^2+4) A = B = C = B Consider the following indefinite integral. ∫(6x^3+3x^2-45x-24)/(x^2-9) dx The integrand decomposes into the form: ax+b+c/(x-3)+d/(x+3) Compute the coefficients: a = b = c = d =
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