Anti derivative of the function x/lnx

  • Context: Undergrad 
  • Thread starter Thread starter Murad A.Omar
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SUMMARY

The anti-derivative of the function x/ln(x) does not have a closed-form solution using elementary functions. However, it can be expressed in terms of the exponential integral function, specifically as -Ei(1, 2ln(x)). This expression allows for the approximation of values related to the integral, highlighting the significance of the Ei function in advanced mathematical theory.

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Murad A.Omar
hi
how are you all
can you help me in finding the anti derivative of the function
x/lnx
 
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As-salaam alaikum!

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

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