What is the integral of 3/((5x-2)^2) ?

The integral of 3/((5x-2)^2) is -3/(5(5x-2))+C

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integral of 3/((5x-2)^2)

\int \frac{3}{( 5 x - 2 ) ^{2}} d x

- \frac{3}{5 ( 5 x - 2 )} + C

Solution steps

\int \frac{3}{( 5 x - 2 ) ^{2}} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{( 5 x - 2 ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{5 u ^{2}} d u

= 3 \cdot \int \frac{1}{5 u ^{2}} d u

Take the constant out:

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

= 3 \cdot \frac{1}{5} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 3 \cdot \frac{1}{5} (- \frac{1}{u})

Substitute back

u = 5 x - 2

= 3 \cdot \frac{1}{5} (- \frac{1}{5 x - 2})

Simplify

3 \cdot \frac{1}{5} (- \frac{1}{5 x - 2}) : - \frac{3}{5 ( 5 x - 2 )}

= - \frac{3}{5 ( 5 x - 2 )}

Add a constant to the solution

= - \frac{3}{5 ( 5 x - 2 )} + C

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What is the integral of 3/((5x-2)^2) ?
The integral of 3/((5x-2)^2) is -3/(5(5x-2))+C