What is the integral of (2x)/(x^4) ?

The integral of (2x)/(x^4) is -1/(x^2)+C

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integral of (2x)/(x^4)

\int \frac{2 x}{x ^{4}} d x

- \frac{1}{x ^{2}} + C

Solution steps

\int \frac{2 x}{x ^{4}} d x

Take the constant out:

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

= 2 \cdot \int \frac{x}{x ^{4}} d x

Cancel the common factor:

x

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

Apply the Power Rule

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

Simplify

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

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

Add a constant to the solution

= - \frac{1}{x ^{2}} + C