What is the integral from 2 to 7 of (-x/7+9/7)-(2/x) ?

The integral from 2 to 7 of (-x/7+9/7)-(2/x) is -2(ln(7)-ln(2))+45/14

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integral from 2 to 7 of (-x/7+9/7)-(2/x)

\int_{2}^{7} (- \frac{x}{7} + \frac{9}{7}) - (\frac{2}{x}) d x

- 2 (ln (7) - ln (2)) + \frac{45}{14}

Decimal Notation

0.70875 \dots

Solution steps

\int_{2}^{7} - \frac{x}{7} + \frac{9}{7} - \frac{2}{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_{2}^{7} \frac{x}{7} d x + \int_{2}^{7} \frac{9}{7} d x - \int_{2}^{7} \frac{2}{x} d x

\int_{2}^{7} \frac{x}{7} d x = \frac{45}{14}

\int_{2}^{7} \frac{9}{7} d x = \frac{45}{7}

\int_{2}^{7} \frac{2}{x} d x = 2 (ln (7) - ln (2))

= - \frac{45}{14} + \frac{45}{7} - 2 (ln (7) - ln (2))

Combine the fractions

- \frac{45}{14} + \frac{45}{7} : \frac{45}{14}

= - 2 (ln (7) - ln (2)) + \frac{45}{14}

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What is the integral from 2 to 7 of (-x/7+9/7)-(2/x) ?
The integral from 2 to 7 of (-x/7+9/7)-(2/x) is -2(ln(7)-ln(2))+45/14