What is the integral from 1 to 27 of (x+1)/(sqrt(x)) ?

The integral from 1 to 27 of (x+1)/(sqrt(x)) is 60sqrt(3)-8/3

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integral from 1 to 27 of (x+1)/(sqrt(x))

\int_{1}^{27} \frac{x + 1}{x} d x

603 - \frac{8}{3}

Decimal

101.25638 \dots

Solution steps

\int_{1}^{27} \frac{x + 1}{x} d x

Expand

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

= \int_{1}^{27} 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_{1}^{27} x d x + \int_{1}^{27} \frac{1}{x} d x

\int_{1}^{27} x d x = 543 - \frac{2}{3}

\int_{1}^{27} \frac{1}{x} d x = 63 - 2

= 543 - \frac{2}{3} + 63 - 2

Simplify

543 - \frac{2}{3} + 63 - 2 : 603 - \frac{8}{3}

= 603 - \frac{8}{3}

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What is the integral from 1 to 27 of (x+1)/(sqrt(x)) ?
The integral from 1 to 27 of (x+1)/(sqrt(x)) is 60sqrt(3)-8/3