What is the integral from 9 to 10 of x/9-9/x ?

The integral from 9 to 10 of x/9-9/x is 19/18-9(ln(10)-2ln(3))

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integral from 9 to 10 of x/9-9/x

\int_{9}^{10} \frac{x}{9} - \frac{9}{x} d x

\frac{19}{18} - 9 (ln (10) - 2 ln (3))

Decimal

0.10731 \dots

Solution steps

\int_{9}^{10} \frac{x}{9} - \frac{9}{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_{9}^{10} \frac{x}{9} d x - \int_{9}^{10} \frac{9}{x} d x

\int_{9}^{10} \frac{x}{9} d x = \frac{19}{18}

\int_{9}^{10} \frac{9}{x} d x = 9 (ln (10) - 2 ln (3))

= \frac{19}{18} - 9 (ln (10) - 2 ln (3))

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What is the integral from 9 to 10 of x/9-9/x ?
The integral from 9 to 10 of x/9-9/x is 19/18-9(ln(10)-2ln(3))