What is the integral from 1 to 3 of e^xln(x) ?

The integral from 1 to 3 of e^xln(x) is e^3ln(3)-\Ei(3)+\Ei(1)

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integral from 1 to 3 of e^xln(x)

\int_{1}^{3} e^{x} ln (x) d x

e^{3} ln (3) - Ei (3) + Ei (1)

Solution steps

\int_{1}^{3} e^{x} ln (x) d x

Apply Integration By Parts

: [e^{x} ln (x) - \int \frac{e ^{x}}{x} d x]_{1}^{3}

= [e^{x} ln (x) - \int \frac{e ^{x}}{x} d x]_{1}^{3}

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

= [e^{x} ln (x) - Ei (x)]_{1}^{3}

Compute the boundaries:

e^{3} ln (3) - Ei (3) + Ei (1)

= e^{3} ln (3) - Ei (3) + Ei (1)

\int_{1}^{3} \frac{2}{x} + 1 d x

\int_{0}^{r} (b r^{2} + cr) 2 π r d r

\int_{0}^{\frac{π}{3}} (cos (x) + sec (x))^{2} d x

\int_{0}^{4} 2 - x d x

\int_{0}^{1} x (x^{2} - 1)^{3} d x

What is the integral from 1 to 3 of e^xln(x) ?
The integral from 1 to 3 of e^xln(x) is e^3ln(3)-\Ei(3)+\Ei(1)