integral, from 0 to infinity, of [ (ln(x))^2 ] / [ 1 + x^2 ] dx

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[imath]\displaystyle{ \int^{\infty }_{0} \dfrac{\left( \ln (x)\right)^{2}}{1+x^{2}}dx }[/imath]

 

[stapel]

[imath]\displaystyle{ \int^{\infty }_{0} \dfrac{\left( \ln (x)\right)^{2}}{1+x^{2}}dx }[/imath]

What are your thoughts? What have you tried? Where are you getting stuck?

Please be complete. Thank you!

 

[topsquark]

[imath]\displaystyle{ \int^{\infty }_{0} \dfrac{\left( \ln (x)\right)^{2}}{1+x^{2}}dx }[/imath]

Unless someone has a trick handy, this is a hellish problem. It does have a nice, and exact, answer, but Mathematica is showing that the indefinite integral is a real monster.

Are you taking a class? If so, what have you been covering? That might give a clue.

-Dan