Problem 5

Question

Find the indefinite integral. $$ \int \frac{x^{2}-4}{x} d x $$

Step-by-Step Solution

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Answer

$\frac{1}{2} x^{2} - 4 \ln|x| + C$

1Step 1: Divide the Terms

Divide each term of numerator individually by the denominator term, separating it into two simpler integrals. This results in the function: $x - \frac{4}{x}$

2Step 2: Integrate each term

We can now take the integral of each term individually. The integral of $x$ is $\frac{1}{2} x^{2}$, and the integral of $\frac{4}{x}$ is $4 \ln|x|$. Applying these rules gives us: $\frac{1}{2} x^{2} - 4 \ln|x|$

3Step 3: Add Constant of Integration

The indefinite integral is ambiguous up to an arbitrary constant. Therefore, we add a constant of integration, denoted as $+ C$, to the result. The solution thus becomes: $\frac{1}{2} x^{2} - 4 \ln|x| + C$

Problem 5

Other exercises in this chapter

Problem 5

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Problem 5

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Problem 5

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