I was trying to evaluate this integral,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int\frac{dx}{\ln x}[/tex]

I substituted [tex]x=e^{i\theta}[/tex] and I get,

[tex]\int\frac{e^{i\theta}}{\theta}d\theta[/tex]

which is,

[tex]\int\frac{\cos \theta}{\theta}+i\frac{\sin \theta}{\theta} \ d\theta[/tex]

[tex]\int\frac{\cos \theta}{\theta} \ d\theta+i\int\frac{\sin \theta}{\theta} \ d\theta[/tex]

[tex]Ci(\theta)+i \ Si(\theta)[/tex]

[tex]Ci(\theta)[/tex] and [tex]Si(\theta)[/tex] are the cosine and sine integrals, respectively.

therefore,

[tex]\int\frac{dx}{\ln x}=Ci(-i\ln x)+i \ Si(-i\ln x)[/tex]

I was just asking if anybody has seen the logarithmic integral( [tex]li(x)[/tex] ) expressed this way.

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# Logarithmic Integral

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