What is the integral of (5x)/(x^2) ?

The integral of (5x)/(x^2) is 5ln|x|+C

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integral of (5x)/(x^2)

\int \frac{5 x}{x ^{2}} d x

5 ln ∣ x ∣ + C

Solution steps

\int \frac{5 x}{x ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{x}{x ^{2}} d x

Cancel the common factor:

x

= 5 \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 ln ∣ x ∣

Add a constant to the solution

= 5 ln ∣ x ∣ + C