What is the integral from 1.1 to 1.3 of e^xln(x) ?

The integral from 1.1 to 1.3 of e^xln(x) is 0.67636…+\Ei(1.1)-\Ei(1.3)

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integral from 1.1 to 1.3 of e^xln(x)

\int_{1.1}^{1.3} e^{x} ln (x) d x

0.67636 \dots + Ei (1.1) - Ei (1.3)

Solution steps

\int_{1.1}^{1.3} e^{x} ln (x) d x

Apply Integration By Parts

: [e^{x} ln (x) - \int \frac{e ^{x}}{x} d x]_{1.1}^{1.3}

= [e^{x} ln (x) - \int \frac{e ^{x}}{x} d x]_{1.1}^{1.3}

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

= [e^{x} ln (x) - Ei (x)]_{1.1}^{1.3}

Compute the boundaries:

0.67636 \dots + Ei (1.1) - Ei (1.3)

= 0.67636 \dots + Ei (1.1) - Ei (1.3)

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What is the integral from 1.1 to 1.3 of e^xln(x) ?
The integral from 1.1 to 1.3 of e^xln(x) is 0.67636…+\Ei(1.1)-\Ei(1.3)