What is the integral from 1 to e of 3/x ?

The integral from 1 to e of 3/x is 3

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integral from 1 to e of 3/x

\int_{1}^{e} \frac{3}{x} d x

3

Solution steps

\int_{1}^{e} \frac{3}{x} d x

Take the constant out:

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

= 3 \cdot \int_{1}^{e} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 3 [ln ∣ x ∣]_{1}^{e}

Compute the boundaries:

1

= 3 \cdot 1

Simplify

= 3