# How do you find the indefinite integral of #int (x^2-6x-20)/(x+5)#?

The answer is

We perform this integral by substitution.

and

Therefore,

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To find the indefinite integral of (\int \frac{x^2-6x-20}{x+5} ), we can use the method of polynomial long division to divide (x^2 - 6x - 20) by (x + 5). Upon performing the division, we'll get a quotient of (x - 11) and a remainder of (0). Thus, the integral simplifies to (\int x - 11 , dx). Integrating each term separately, we get (\frac{x^2}{2} - 11x + C), where (C) is the constant of integration. Therefore, the indefinite integral of (\frac{x^2-6x-20}{x+5}) is (\frac{x^2}{2} - 11x + C).

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