What is the integral of-(1000)/((2x+50)^2) ?

The integral of-(1000)/((2x+50)^2) is (250)/(x+25)+C

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integral of-(1000)/((2x+50)^2)

\int - \frac{1000}{( 2 x + 50 ) ^{2}} d x

\frac{250}{x + 25} + C

Solution steps

\int - \frac{1000}{( 2 x + 50 ) ^{2}} d x

Take the constant out:

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

= - 1000 \cdot \int \frac{1}{( 2 x + 50 ) ^{2}} d x

Apply u-substitution

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

= - 1000 \cdot \int \frac{1}{2 u ^{2}} d u

Take the constant out:

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

= - 1000 \cdot \frac{1}{2} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - 1000 \cdot \frac{1}{2} (- \frac{1}{u})

Substitute back

u = 2 x + 50

= - 1000 \cdot \frac{1}{2} (- \frac{1}{2 x + 50})

Simplify

- 1000 \cdot \frac{1}{2} (- \frac{1}{2 x + 50}) : \frac{250}{x + 25}

= \frac{250}{x + 25}

Add a constant to the solution

= \frac{250}{x + 25} + C

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What is the integral of-(1000)/((2x+50)^2) ?
The integral of-(1000)/((2x+50)^2) is (250)/(x+25)+C