What is the integral from 1 to 4 of (5/x) ?

The integral from 1 to 4 of (5/x) is 10ln(2)

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integral from 1 to 4 of (5/x)

\int_{1}^{4} (\frac{5}{x}) d x

10 ln (2)

Decimal

6.93147 \dots

Solution steps

\int_{1}^{4} \frac{5}{x} d x

Take the constant out:

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

= 5 \cdot \int_{1}^{4} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 [ln ∣ x ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

= 5 \cdot 2 ln (2)

Simplify

= 10 ln (2)

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

\int_{0}^{1} (ln (x))^{4} d x

\int_{2}^{3} (2 x - 5)^{4} d x

\int_{1}^{3} (- 2 x + 1) d x

\int_{- 1}^{1} 6 x^{2} d x

What is the integral from 1 to 4 of (5/x) ?
The integral from 1 to 4 of (5/x) is 10ln(2)