Solve the following integral. The answer can be determined by rules of antidifferentiation, but some algebra may be required beforehand.
\[
\int \frac{x^{2}-9}{x-3} d x
\]
\[
\int \frac{x^{2}-9}{x-3} d x=
\]

Answer

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Answer

\(\boxed{\frac{x^{2}}{2} + 3x + C}\) is the final answer, where \(C\) is the constant of integration.

Steps

Step 1 ：Given the integral \(\int \frac{x^{2}-9}{x-3} dx\)

Step 2 ：Factor the numerator to get \((x-3)(x+3)\), so the integral becomes \(\int \frac{(x-3)(x+3)}{x-3} dx\)

Step 3 ：Simplify the integral to \(\int (x+3) dx\)

Step 4 ：Apply the power rule for integration to get \(\frac{x^{2}}{2} + 3x\)

Step 5 ：\(\boxed{\frac{x^{2}}{2} + 3x + C}\) is the final answer, where \(C\) is the constant of integration.