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

The integral from 2 to 3 of (x+1)/(sqrt(x)) is -(4sqrt(2))/3+4sqrt(3)-2sqrt(2)

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

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

- \frac{4 2}{3} + 43 - 22

Decimal Notation

2.21415 \dots

Solution steps

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

Expand

\frac{x + 1}{x} : x + \frac{1}{x}

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

\int_{2}^{3} x d x = 23 - \frac{4 2}{3}

\int_{2}^{3} \frac{1}{x} d x = 23 - 22

= 23 - \frac{4 2}{3} + 23 - 22

Simplify

= - \frac{4 2}{3} + 43 - 22

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