What is the integral from 1 to 25 of 2/x ?

The integral from 1 to 25 of 2/x is 4ln(5)

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integral from 1 to 25 of 2/x

\int_{1}^{25} \frac{2}{x} d x

4 ln (5)

Decimal Notation

6.43775 \dots

Solution steps

\int_{1}^{25} \frac{2}{x} d x

Take the constant out:

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

= 2 \cdot \int_{1}^{25} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 [ln ∣ x ∣]_{1}^{25}

Compute the boundaries:

2 ln (5)

= 2 \cdot 2 ln (5)

Simplify

= 4 ln (5)

x \to + 0 lim (\frac{x ^{2}}{1 - cos ( x )})

\frac{d y}{d x} = \frac{5 x}{7 y}

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

\int - 2 x + 6 x^{2} - 4 x^{3} + C d x

\frac{\partial}{\partial y} (ln (1 + x y))

What is the integral from 1 to 25 of 2/x ?
The integral from 1 to 25 of 2/x is 4ln(5)