Anti derivative of the function x/lnx

[Murad A.Omar]

hi
how are you all
can you help me in finding the anti derivative of the function
x/lnx

 

[damgo]

As-salaam alaikum!

There's no closed-form solution for that integral, unfortunately.

 

[rutwig]

Although no elementary functions can be found, a closed expression is

[inte]x/Ln(x)dx= -Ei(1,2Ln(x)),

so that you can approximate the values of the function.

P.S: It is not infortunate (for me) that there is no primitive, since the Ei function is an essential ingredient of the theory and has led to marvellous new insights.