What is the integral from 2 to 7 of (x+6)/(sqrt(x)) ?

The integral from 2 to 7 of (x+6)/(sqrt(x)) is (14sqrt(7)-4sqrt(2))/3+6(2sqrt(7)-2sqrt(2))

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integral from 2 to 7 of (x+6)/(sqrt(x))

\int_{2}^{7} \frac{x + 6}{x} d x

\frac{14 7 - 4 2}{3} + 6 (27 - 22)

Decimal Notation

25.23967 \dots

Solution steps

\int_{2}^{7} \frac{x + 6}{x} d x

Expand

\frac{x + 6}{x} : x + \frac{6}{x}

= \int_{2}^{7} x + \frac{6}{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}^{7} x d x + \int_{2}^{7} \frac{6}{x} d x

\int_{2}^{7} x d x = \frac{14 7 - 4 2}{3}

\int_{2}^{7} \frac{6}{x} d x = 6 (27 - 22)

= \frac{14 7 - 4 2}{3} + 6 (27 - 22)

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What is the integral from 2 to 7 of (x+6)/(sqrt(x)) ?
The integral from 2 to 7 of (x+6)/(sqrt(x)) is (14sqrt(7)-4sqrt(2))/3+6(2sqrt(7)-2sqrt(2))