What is the integral from 0 to 1 of e^xln(x) ?

The integral from 0 to 1 of e^xln(x) is diverges

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integral from 0 to 1 of e^xln(x)

\int_{0}^{1} e^{x} ln (x) d x

diverges

Solution steps

\int_{0}^{1} e^{x} ln (x) d x

Apply Integration By Parts

: [e^{x} ln (x) - \int \frac{e ^{x}}{x} d x]_{0}^{1}

= [e^{x} ln (x) - \int \frac{e ^{x}}{x} d x]_{0}^{1}

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

= [e^{x} ln (x) - Ei (x)]_{0}^{1}

Compute the boundaries:

diverges

= diverges

\int_{1}^{x} 2 - x d x

\int_{2}^{6} (x + 3)^{2} d x

\int_{2 t}^{3 t} \frac{sin ( x )}{2 x} d x

\int_{0}^{1} 2 y^{3} d y

\int_{- 2}^{0} x^{3} + x^{2} - 2 x d x

What is the integral from 0 to 1 of e^xln(x) ?
The integral from 0 to 1 of e^xln(x) is diverges