# Find the integral of (x^2 - 14x + 10)/(x + 12) dx.

## Question:

Find {eq}\; \int \frac{x^2 - 14x + 10}{x + 12} \, \mathrm{d}x {/eq}.

## Answer and Explanation:

{eq}\int \frac{x^2-14x+10}{x+12}dx\\ \text{Substituting:}\\ t=x+12\\ =\int \frac{t^2-38t+322}{t}dt\\ =\int \left (t-38+\frac{322}{t} \right )dt\\ \text{Applying formulas:}\\ =\frac{t^2}{2}-38t+322\ln t\\ \text{Applying the constant of integration}\\ =\frac{(x+12)^2}{2}-38(x+2)+322\ln (x+12)+C {/eq}

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