What is the integral of 1/(-3x^2) ?

The integral of 1/(-3x^2) is 1/(3x)+C

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integral of 1/(-3x^2)

\int \frac{1}{- 3 x ^{2}} d x

\frac{1}{3 x} + C

Solution steps

\int \frac{1}{- 3 x ^{2}} d x

Take the constant out:

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

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

Simplify

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

Apply the Power Rule

: - \frac{1}{x}

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

Simplify

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

= \frac{1}{3 x}

Add a constant to the solution

= \frac{1}{3 x} + C

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