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Popular Calculus >

integral of ((y-3))/y

Solution

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

Solution

y - 3 ln ∣ y ∣ + C

Solution steps

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

Expand

\frac{y - 3}{y} : 1 - \frac{3}{y}

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

\int 1 d y = y

\int \frac{3}{y} d y = 3 ln ∣ y ∣

= y - 3 ln ∣ y ∣

Add a constant to the solution

= y - 3 ln ∣ y ∣ + C

Graph

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Frequently Asked Questions (FAQ)

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