What is the integral of (3x)/(x^3) ?

The integral of (3x)/(x^3) is -3/x+C

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integral of (3x)/(x^3)

\int \frac{3 x}{x ^{3}} d x

- \frac{3}{x} + C

Solution steps

\int \frac{3 x}{x ^{3}} d x

Take the constant out:

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

= 3 \cdot \int \frac{x}{x ^{3}} d x

Cancel the common factor:

x

= 3 \cdot \int \frac{1}{x ^{2}} d x

Apply the Power Rule

: - \frac{1}{x}

= 3 (- \frac{1}{x})

Simplify

3 (- \frac{1}{x}) : - \frac{3}{x}

= - \frac{3}{x}

Add a constant to the solution

= - \frac{3}{x} + C

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