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 Notation

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

\frac{d y}{d x} - \frac{2 y}{x} = x^{2} sin (3 x)

\int \frac{cos ( 4 x )}{1 + sin ^{2} ( 4 x )} d x

\int_{0}^{10} 1

\frac{d}{d x} (- \frac{x}{4 - x ^{2}})

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