What is the integral from 1 to 4 of 4/x-x/4 ?

The integral from 1 to 4 of 4/x-x/4 is 8ln(2)-15/8

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integral from 1 to 4 of 4/x-x/4

\int_{1}^{4} \frac{4}{x} - \frac{x}{4} d x

8 ln (2) - \frac{15}{8}

Decimal

3.67017 \dots

Solution steps

\int_{1}^{4} \frac{4}{x} - \frac{x}{4} 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}^{4} \frac{4}{x} d x - \int_{1}^{4} \frac{x}{4} d x

\int_{1}^{4} \frac{4}{x} d x = 8 ln (2)

\int_{1}^{4} \frac{x}{4} d x = \frac{15}{8}

= 8 ln (2) - \frac{15}{8}

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What is the integral from 1 to 4 of 4/x-x/4 ?
The integral from 1 to 4 of 4/x-x/4 is 8ln(2)-15/8