MHB Solve Int. xe^xlnx Difficult Integral

[Maged Saeed]

Can anyone help me Evaluating this integral!
$$\int xe^xlnxdx$$

 

[chisigma]

Can anyone help me Evaluating this integral!
$$\int xe^xlnxdx$$

Integrating by parts You obtain...

$\displaystyle \int x\ e^x\ \ln x\ dx = (x-1)\ e^{x}\ \ln x - \int \frac{x-1}{x}\ e^{x}\ dx = (x-1)\ e^{x}\ \ln x - e^{x} + \text{Ei}\ (x) + c\ (1)$

... where $\text{Ei} (x)$ is the 'Exponential Integral Function'...

Kind regards

$\chi$ $\sigma$