What is the integral from 1/2 to 1 of 1/(x^2)-1/x ?

The integral from 1/2 to 1 of 1/(x^2)-1/x is 1-ln(2)

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integral from 1/2 to 1 of 1/(x^2)-1/x

\int_{\frac{1}{2}}^{1} \frac{1}{x ^{2}} - \frac{1}{x} d x

1 - ln (2)

Decimal Notation

0.30685 \dots

Solution steps

\int_{\frac{1}{2}}^{1} \frac{1}{x ^{2}} - \frac{1}{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_{\frac{1}{2}}^{1} \frac{1}{x ^{2}} d x - \int_{\frac{1}{2}}^{1} \frac{1}{x} d x

\int_{\frac{1}{2}}^{1} \frac{1}{x ^{2}} d x = 1

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

= 1 - ln (2)

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