# Determine the following indefinite integral. \int \frac{x^{5}-3}{x}dx

Determine the following indefinite integral.
$\int \frac{{x}^{5}-3}{x}dx$
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Theirl1972
Step 1
We have to determine the indefinite integral:
$\int \frac{{x}^{5}-3}{x}dx$
Step 2
We can write
So, $\int \frac{{x}^{5}-3}{x}dx=\int \left({x}^{4}-\frac{3}{x}\right)dx$
$=\int {x}^{4}dx-\int \frac{3}{x}dx$
$=\frac{{x}^{5}}{5}-3\mathrm{ln}\left(|x|\right)+C$
Therefore, $\int \frac{{x}^{5}-3}{x}dx=\frac{{x}^{5}}{5}-3\mathrm{ln}\left(|x|\right)+C$
###### Not exactly what you’re looking for?
Jennifer Hill
Step 1: Simplify $\frac{{x}^{5}-3}{x}\to {x}^{4}-\frac{3}{x}$.
$\int {x}^{4}-\frac{3}{x}dx$
Step 2: Use Sum Rule: $\int f\left(x\right)+g\left(x\right)dx=\int f\left(x\right)dx+\int g\left(x\right)dx$.
$\int {x}^{4}dx-\int \frac{3}{x}dx$
Step 3: Use Power Rule: $\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+C$.
$\frac{{x}^{5}}{5}-\int \frac{3}{x}dx$
Step 4: Use Constant Factor Rule: $\int cf\left(x\right)dx=f\int f\left(x\right)dx$.
$\frac{{x}^{5}}{5}-3\int \frac{1}{x}dx$
Step 5: The derivative of .
$\frac{{x}^{5}}{5}-3\mathrm{ln}x$
$\frac{{x}^{5}}{5}-3\mathrm{ln}x+C$