What is the integral from 4 to 9 of (9x+1)/(sqrt(x)) ?

The integral from 4 to 9 of (9x+1)/(sqrt(x)) is 116

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integral from 4 to 9 of (9x+1)/(sqrt(x))

\int_{4}^{9} \frac{9 x + 1}{x} d x

116

Solution steps

\int_{4}^{9} \frac{9 x + 1}{x} d x

Expand

\frac{9 x + 1}{x} : 9 x + \frac{1}{x}

= \int_{4}^{9} 9 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_{4}^{9} 9 x d x + \int_{4}^{9} \frac{1}{x} d x

\int_{4}^{9} 9 x d x = 114

\int_{4}^{9} \frac{1}{x} d x = 2

= 114 + 2

Simplify

= 116

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What is the integral from 4 to 9 of (9x+1)/(sqrt(x)) ?
The integral from 4 to 9 of (9x+1)/(sqrt(x)) is 116