What is the integral from 1/3 to 3 of 1/(4x) ?

The integral from 1/3 to 3 of 1/(4x) is 1/2 ln(3)

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integral from 1/3 to 3 of 1/(4x)

\int_{\frac{1}{3}}^{3} \frac{1}{4 x} d x

\frac{1}{2} ln (3)

Decimal

0.54930 \dots

Solution steps

\int_{\frac{1}{3}}^{3} \frac{1}{4 x} d x

Take the constant out:

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

= \frac{1}{4} \cdot \int_{\frac{1}{3}}^{3} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{4} [ln ∣ x ∣]_{\frac{1}{3}}^{3}

Compute the boundaries:

2 ln (3)

= \frac{1}{4} \cdot 2 ln (3)

Simplify

= \frac{1}{2} ln (3)

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What is the integral from 1/3 to 3 of 1/(4x) ?
The integral from 1/3 to 3 of 1/(4x) is 1/2 ln(3)