What is the integral of ((y-2))/((y+3)) ?

The integral of ((y-2))/((y+3)) is -5ln|y+3|+y+C

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integral of ((y-2))/((y+3))

\int \frac{( y - 2 )}{( y + 3 )} d y

- 5 ln ∣ y + 3 ∣ + y + C

Solution steps

\int \frac{y - 2}{y + 3} d y

\frac{y - 2}{y + 3} = - \frac{5}{y + 3} + 1

= \int - \frac{5}{y + 3} + 1 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{5}{y + 3} d y + \int 1 d y

\int \frac{5}{y + 3} d y = 5 ln ∣ y + 3 ∣

\int 1 d y = y

= - 5 ln ∣ y + 3 ∣ + y

Add a constant to the solution

= - 5 ln ∣ y + 3 ∣ + y + C

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What is the integral of ((y-2))/((y+3)) ?
The integral of ((y-2))/((y+3)) is -5ln|y+3|+y+C