What is the integral from 1 to r of (20)/x ?

The integral from 1 to r of (20)/x is 20ln|r|

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integral from 1 to r of (20)/x

\int_{1}^{r} \frac{20}{x} d x

20 ln ∣ r ∣

Solution steps

\int_{1}^{r} \frac{20}{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 20 \cdot \int_{1}^{r} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 20 [ln ∣ x ∣]_{1}^{r}

Compute the boundaries:

ln ∣ r ∣

= 20 ln ∣ r ∣

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What is the integral from 1 to r of (20)/x ?
The integral from 1 to r of (20)/x is 20ln|r|