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Chapter 4: Problem 9

Find the indefinite integral. $$ \int \frac{x^{3}-3 x^{2}+5}{x-3} d x $$

Short Answer

Expert verified
The integral of the given function is \(x^3/3 + 3x^2/2 + 14x - 42 \ln|x - 3| + C\), where \(C\) is the constant of integration.

Step by step solution

01

Polynomial Division

Divide the numerator polynomial with the denominator in the integral, which gives us \(x^2 + 3x + 14 - 42/(x - 3)\).
02

Solving the Individual Integrals

Now we find the integral of each individual term separately. The integral of \(x^2\) is \(x^3/3\), the integral of \(3x\) is \(3x^2/2\) the integral of \(14\) is \(14x\), and the integral of \(-42/(x - 3)\) is \(-42 \ln|x - 3|\).
03

Combining the Integrals

Combine all individual integrals with the respective coefficients to get the final result.

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