What is the integral of e^x*ln(x) ?

The integral of e^x*ln(x) is e^xln(x)-\Ei(x)+C

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integral of e^x*ln(x)

\int e^{x} \cdot ln (x) d x

e^{x} ln (x) - Ei (x) + C

Solution steps

\int e^{x} ln (x) d x

Apply Integration By Parts

: e^{x} ln (x) - \int \frac{e ^{x}}{x} d x

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

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

= e^{x} ln (x) - Ei (x)

Add a constant to the solution

= e^{x} ln (x) - Ei (x) + C

n = 1 \sum \infty \frac{n}{e ^{n^{2}}}

\frac{\partial}{\partial y} (e^{x y} - (x + 1) cos (y))

x \to 0 lim (\frac{x ^{3} + 7 x}{x})

y = x^{2} - 5, y = 4

\int_{6}^{8} \frac{64}{( x - 6 ) ^{3}} d x

What is the integral of e^x*ln(x) ?
The integral of e^x*ln(x) is e^xln(x)-\Ei(x)+C