What is the integral from 1 to e^2 of 3/x ?

The integral from 1 to e^2 of 3/x is 6

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integral from 1 to e^2 of 3/x

\int_{1}^{e^{2}} \frac{3}{x} d x

6

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 3 [ln ∣ x ∣]_{1}^{e^{2}}

Compute the boundaries:

2

= 3 \cdot 2

Simplify

= 6

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What is the integral from 1 to e^2 of 3/x ?
The integral from 1 to e^2 of 3/x is 6