# How do you integrate #(5x^2+7x-4)/(x^3+4x^2)# using partial fractions?

The answer is

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To integrate (\frac{5x^2+7x-4}{x^3+4x^2}) using partial fractions, you would first factor the denominator, then express the rational function as a sum of simpler fractions. In this case, the denominator (x^3 + 4x^2) factors into (x^2(x + 4)). The decomposition into partial fractions would have the following form:

[\frac{5x^2+7x-4}{x^3+4x^2} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x + 4}]

Then, you would solve for the unknown coefficients (A), (B), and (C) by equating coefficients. After finding the values of (A), (B), and (C), you would integrate each term separately.

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