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

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

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

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

- \frac{1}{3 ( 3 x - 2 )} + C

Solution steps

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

Apply u-substitution

= \int \frac{1}{3 u ^{2}} d u

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}{u ^{2}} d u

Apply the Power Rule

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

Substitute back

u = 3 x - 2

= \frac{1}{3} (- \frac{1}{3 x - 2})

Simplify

\frac{1}{3} (- \frac{1}{3 x - 2}) : - \frac{1}{3 ( 3 x - 2 )}

= - \frac{1}{3 ( 3 x - 2 )}

Add a constant to the solution

= - \frac{1}{3 ( 3 x - 2 )} + C

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