What is the integral from 1 to 9 of 9/x-x/9 ?

The integral from 1 to 9 of 9/x-x/9 is 18ln(3)-40/9

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integral from 1 to 9 of 9/x-x/9

\int_{1}^{9} \frac{9}{x} - \frac{x}{9} d x

18 ln (3) - \frac{40}{9}

Decimal

15.33057 \dots

Solution steps

\int_{1}^{9} \frac{9}{x} - \frac{x}{9} 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}^{9} \frac{9}{x} d x - \int_{1}^{9} \frac{x}{9} d x

\int_{1}^{9} \frac{9}{x} d x = 18 ln (3)

\int_{1}^{9} \frac{x}{9} d x = \frac{40}{9}

= 18 ln (3) - \frac{40}{9}

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What is the integral from 1 to 9 of 9/x-x/9 ?
The integral from 1 to 9 of 9/x-x/9 is 18ln(3)-40/9