What is the integral from 1 to e of (y^2+2)/y ?

The integral from 1 to e of (y^2+2)/y is (e^2-1)/2+2

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integral from 1 to e of (y^2+2)/y

\int_{1}^{e} \frac{y ^{2} + 2}{y} d y

\frac{e ^{2} - 1}{2} + 2

Decimal Notation

5.19452 \dots

Solution steps

\int_{1}^{e} \frac{y ^{2} + 2}{y} d y

Expand

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

= \int_{1}^{e} y + \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}^{e} y d y + \int_{1}^{e} \frac{2}{y} d y

\int_{1}^{e} y d y = \frac{e ^{2} - 1}{2}

\int_{1}^{e} \frac{2}{y} d y = 2

= \frac{e ^{2} - 1}{2} + 2

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What is the integral from 1 to e of (y^2+2)/y ?
The integral from 1 to e of (y^2+2)/y is (e^2-1)/2+2