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

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

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

\int_{1}^{4} \frac{3}{2 x} d x

3 ln (2)

Decimal

2.07944 \dots

Solution steps

\int_{1}^{4} \frac{3}{2 x} d x

Take the constant out:

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

= \frac{3}{2} \cdot \int_{1}^{4} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{3}{2} [ln ∣ x ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

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

Simplify

= 3 ln (2)

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