What is the integral from 1 to 7 of x/7-7/x ?

The integral from 1 to 7 of x/7-7/x is 24/7-7ln(7)

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integral from 1 to 7 of x/7-7/x

\int_{1}^{7} \frac{x}{7} - \frac{7}{x} d x

\frac{24}{7} - 7 ln (7)

Decimal

- 10.19279 \dots

Solution steps

\int_{1}^{7} \frac{x}{7} - \frac{7}{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}^{7} \frac{x}{7} d x - \int_{1}^{7} \frac{7}{x} d x

\int_{1}^{7} \frac{x}{7} d x = \frac{24}{7}

\int_{1}^{7} \frac{7}{x} d x = 7 ln (7)

= \frac{24}{7} - 7 ln (7)

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What is the integral from 1 to 7 of x/7-7/x ?
The integral from 1 to 7 of x/7-7/x is 24/7-7ln(7)