What is the integral from 1 to 16 of 1/(2x) ?

The integral from 1 to 16 of 1/(2x) is 2ln(2)

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integral from 1 to 16 of 1/(2x)

\int_{1}^{16} \frac{1}{2 x} d x

2 ln (2)

Decimal Notation

1.38629 \dots

Solution steps

\int_{1}^{16} \frac{1}{2 x} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{16} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{2} [ln ∣ x ∣]_{1}^{16}

Compute the boundaries:

4 ln (2)

= \frac{1}{2} \cdot 4 ln (2)

Simplify

= 2 ln (2)

\int \frac{- x + 8}{- x ^{2} - x + 8} d x

x \to 1 lim (\frac{1 + x}{1 - x})

\frac{1}{1 + 1 x}

y^{^{'}} + t y = t

x^{2} - 3

What is the integral from 1 to 16 of 1/(2x) ?
The integral from 1 to 16 of 1/(2x) is 2ln(2)