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

The integral of 1/((3x)^2) is -1/(9x)+C

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integral of 1/((3x)^2)

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

- \frac{1}{9 x} + C

Solution steps

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

Apply Integration By Parts

= \frac{1}{9 x} - \int - \frac{2}{9 x ^{2}} d x

\int - \frac{2}{9 x ^{2}} d x = \frac{2}{9 x}

= \frac{1}{9 x} - \frac{2}{9 x}

Simplify

= - \frac{1}{9 x}

Add a constant to the solution

= - \frac{1}{9 x} + C