What is the integral of (3x)/(x^4) ?

The integral of (3x)/(x^4) is -3/(2x^2)+C

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integral of (3x)/(x^4)

\int \frac{3 x}{x ^{4}} d x

- \frac{3}{2 x ^{2}} + C

Solution steps

\int \frac{3 x}{x ^{4}} 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 ^{4}} d x

Cancel the common factor:

x

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

Apply the Power Rule

: - \frac{1}{2 x ^{2}}

= 3 (- \frac{1}{2 x ^{2}})

Simplify

3 (- \frac{1}{2 x ^{2}}) : - \frac{3}{2 x ^{2}}

= - \frac{3}{2 x ^{2}}

Add a constant to the solution

= - \frac{3}{2 x ^{2}} + C

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