What is the integral from 1 to e of 5/x ?

The integral from 1 to e of 5/x is 5

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integral from 1 to e of 5/x

\int_{1}^{e} \frac{5}{x} d x

5

Solution steps

\int_{1}^{e} \frac{5}{x} d x

Take the constant out:

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

= 5 \cdot \int_{1}^{e} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 [ln ∣ x ∣]_{1}^{e}

Compute the boundaries:

1

= 5 \cdot 1

Simplify

= 5