What is the integral from 1 to 5 of (3/x) ?

The integral from 1 to 5 of (3/x) is 3ln(5)

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integral from 1 to 5 of (3/x)

\int_{1}^{5} (\frac{3}{x}) d x

3 ln (5)

Decimal

4.82831 \dots

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 3 [ln ∣ x ∣]_{1}^{5}

Compute the boundaries:

ln (5)

= 3 ln (5)

\int_{0}^{1} e^{10 x - 9} d x

\int_{0.5}^{1} ln (x) + x d x

\int_{0}^{2} 3 x (x - 3) d x

\int_{0}^{4} 2 x + 2 d x

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

What is the integral from 1 to 5 of (3/x) ?
The integral from 1 to 5 of (3/x) is 3ln(5)