What is the integral of ((125)/((5x-300)^2)) ?

The integral of ((125)/((5x-300)^2)) is -5/(x-60)+C

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integral of ((125)/((5x-300)^2))

\int (\frac{125}{( 5 x - 300 ) ^{2}}) d x

- \frac{5}{x - 60} + C

Solution steps

\int \frac{125}{( 5 x - 300 ) ^{2}} d x

Take the constant out:

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

= 125 \cdot \int \frac{1}{( 5 x - 300 ) ^{2}} d x

Apply u-substitution

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

= 125 \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

= 125 \cdot \frac{1}{5} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 125 \cdot \frac{1}{5} (- \frac{1}{u})

Substitute back

u = 5 x - 300

= 125 \cdot \frac{1}{5} (- \frac{1}{5 x - 300})

Simplify

125 \cdot \frac{1}{5} (- \frac{1}{5 x - 300}) : - \frac{5}{x - 60}

= - \frac{5}{x - 60}

Add a constant to the solution

= - \frac{5}{x - 60} + C

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What is the integral of ((125)/((5x-300)^2)) ?
The integral of ((125)/((5x-300)^2)) is -5/(x-60)+C