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

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

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

\int_{1}^{3} \frac{x ^{2} + 2}{x} d x

4 + 2 ln (3)

Decimal

6.19722 \dots

Solution steps

\int_{1}^{3} \frac{x ^{2} + 2}{x} d x

Expand

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

= \int_{1}^{3} x + \frac{2}{x} d x

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} x d x + \int_{1}^{3} \frac{2}{x} d x

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

\int_{1}^{3} \frac{2}{x} d x = 2 ln (3)

= 4 + 2 ln (3)

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