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

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

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

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

\frac{2}{5 x} + C

Solution steps

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

Take the constant out:

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

= \frac{- 2}{5} \cdot \int \frac{1}{x ^{2}} d x

Simplify

= (- \frac{2}{5}) \cdot \int \frac{1}{x ^{2}} d x

Apply the Power Rule

: - \frac{1}{x}

= (- \frac{2}{5}) (- \frac{1}{x})

Simplify

(- \frac{2}{5}) (- \frac{1}{x}) : \frac{2}{5 x}

= \frac{2}{5 x}

Add a constant to the solution

= \frac{2}{5 x} + C

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