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

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

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integral of-y/((x+2)^2)

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

\frac{y}{2 + x} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

Apply the Power Rule

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

Substitute back

u = 2 + x

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

Simplify

- y (- \frac{1}{2 + x}) : \frac{y}{2 + x}

= \frac{y}{2 + x}

Add a constant to the solution

= \frac{y}{2 + x} + C