What is the integral from e to 4 of 1/(2x) ?

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

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integral from e to 4 of 1/(2x)

\int_{e}^{4} \frac{1}{2 x} d x

ln (2) - \frac{1}{2}

Decimal

0.19314 \dots

Solution steps

\int_{e}^{4} \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_{e}^{4} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{2} [ln ∣ x ∣]_{e}^{4}

Compute the boundaries:

2 ln (2) - 1

= \frac{1}{2} (2 ln (2) - 1)

Simplify

= ln (2) - \frac{1}{2}

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

\int_{3}^{5} \frac{x}{x - 3} d x

\int_{1}^{\infty} x^{- p} d x

\int_{- 5}^{6} ∣ x ∣ d x

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

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