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

The integral from 1 to 4 of (e^x)/(2x) is 1/2 (\Ei(4)-\Ei(1))

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

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

\frac{1}{2} (Ei (4) - Ei (1))

Solution steps

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

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= \frac{1}{2} [Ei (x)]_{1}^{4}

Compute the boundaries:

Ei (4) - Ei (1)

= \frac{1}{2} (Ei (4) - Ei (1))

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