What is the integral from 1 to 6 of x/6-6/x ?

The integral from 1 to 6 of x/6-6/x is 35/12-6ln(6)

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integral from 1 to 6 of x/6-6/x

\int_{1}^{6} \frac{x}{6} - \frac{6}{x} d x

\frac{35}{12} - 6 ln (6)

Decimal

- 7.83389 \dots

Solution steps

\int_{1}^{6} \frac{x}{6} - \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_{1}^{6} \frac{x}{6} d x - \int_{1}^{6} \frac{6}{x} d x

\int_{1}^{6} \frac{x}{6} d x = \frac{35}{12}

\int_{1}^{6} \frac{6}{x} d x = 6 ln (6)

= \frac{35}{12} - 6 ln (6)

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What is the integral from 1 to 6 of x/6-6/x ?
The integral from 1 to 6 of x/6-6/x is 35/12-6ln(6)