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))

integral

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

- \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

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

\frac{( x ^{5} - 1 )}{x - 1}

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\frac{( x ^{3} + 4 )}{x}

arcsinh (x^{0.5})