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Popular >

integral of (y+2)/y

Solution

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

Solution

y + 2 ln ∣ y ∣ + C

Solution steps

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

Expand

\frac{y + 2}{y} : 1 + \frac{2}{y}

= \int 1 + \frac{2}{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{2}{y} d y

\int 1 d y = y

\int \frac{2}{y} d y = 2 ln ∣ y ∣

= y + 2 ln ∣ y ∣

Add a constant to the solution

= y + 2 ln ∣ y ∣ + C

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area x=y,4x+y^2=12 area

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Frequently Asked Questions (FAQ)

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