What is the integral from 1 to 3 of (z^2+5)/z ?

The integral from 1 to 3 of (z^2+5)/z is 4+5ln(3)

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integral from 1 to 3 of (z^2+5)/z

\int_{1}^{3} \frac{z ^{2} + 5}{z} d z

4 + 5 ln (3)

Decimal

9.49306 \dots

Solution steps

\int_{1}^{3} \frac{z ^{2} + 5}{z} d z

Expand

\frac{z ^{2} + 5}{z} : z + \frac{5}{z}

= \int_{1}^{3} z + \frac{5}{z} d z

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}^{3} z d z + \int_{1}^{3} \frac{5}{z} d z

\int_{1}^{3} z d z = 4

\int_{1}^{3} \frac{5}{z} d z = 5 ln (3)

= 4 + 5 ln (3)

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What is the integral from 1 to 3 of (z^2+5)/z ?
The integral from 1 to 3 of (z^2+5)/z is 4+5ln(3)