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

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

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

\int_{1}^{5} \frac{x ^{2} + 2}{x} d x

12 + 2 ln (5)

Decimal

15.21887 \dots

Solution steps

\int_{1}^{5} \frac{x ^{2} + 2}{x} d x

Expand

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

= \int_{1}^{5} 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}^{5} x d x + \int_{1}^{5} \frac{2}{x} d x

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

\int_{1}^{5} \frac{2}{x} d x = 2 ln (5)

= 12 + 2 ln (5)

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