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

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

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integral from 1 to 4 of 1/(5x)

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

\frac{2}{5} ln (2)

Decimal

0.27725 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{5} [ln ∣ x ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

= \frac{1}{5} \cdot 2 ln (2)

Simplify

= \frac{2}{5} ln (2)

\int_{0}^{1} \frac{1}{cos ( x )} d x

\int_{0}^{0.5} 2 y d y

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

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

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

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