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

The integral from 1 to 5 of (z^2+4)/z is 12+4ln(5)

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integral from 1 to 5 of (z^2+4)/z

\int_{1}^{5} \frac{z ^{2} + 4}{z} d z

12 + 4 ln (5)

Solution steps

\int_{1}^{5} \frac{z ^{2} + 4}{z} d z

Expand

\frac{z ^{2} + 4}{z} : z + \frac{4}{z}

= \int_{1}^{5} z + \frac{4}{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}^{5} z d z + \int_{1}^{5} \frac{4}{z} d z

\int_{1}^{5} z d z = 12

\int_{1}^{5} \frac{4}{z} d z = 4 ln (5)

= 12 + 4 ln (5)

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What is the integral from 1 to 5 of (z^2+4)/z ?
The integral from 1 to 5 of (z^2+4)/z is 12+4ln(5)