What is the integral of e^{x^2}*xln(x) ?

The integral of e^{x^2}*xln(x) is 1/2 e^{x^2}ln(x)-1/4 \Ei(x^2)+C

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integral of e^{x^2}*xln(x)

\int e^{x^{2}} \cdot x ln (x) d x

\frac{1}{2} e^{x^{2}} ln (x) - \frac{1}{4} Ei (x^{2}) + C

Solution steps

\int e^{x^{2}} x ln (x) d x

Apply Integration By Parts

= \frac{1}{2} e^{x^{2}} ln (x) - \int \frac{e ^{x^{2}}}{2 x} d x

\int \frac{e ^{x^{2}}}{2 x} d x = \frac{1}{4} Ei (x^{2})

= \frac{1}{2} e^{x^{2}} ln (x) - \frac{1}{4} Ei (x^{2})

Add a constant to the solution

= \frac{1}{2} e^{x^{2}} ln (x) - \frac{1}{4} Ei (x^{2}) + C

What is the integral of e^{x^2}*xln(x) ?
The integral of e^{x^2}*xln(x) is 1/2 e^{x^2}ln(x)-1/4 \Ei(x^2)+C