A friend gave me this integral and I am having nightmares since. The integral looks like:

$$\int_0^\infty \frac{\ln(1+x-\sqrt{2x})}{1+x^2}\ \mathrm dx$$

Mathematica gives a solution of $0$ but any procedure to get the result eludes me. I found a messy solution with substitutions and by parts( which I will probably add in an edit later because it's too messy to even write ).

A better ( preferably quicker ) solution using any method ( differentiation under integral sign, complex analysis, vector calculus etc ) would be rather helpful. Any input is appreciated!

  • $\begingroup$ Ah I did not see the duplicate question ( the mobile does not show suggestions :P ). Thanks to all for finding the required question with the solution. Does this question stay or can I delete this? $\endgroup$ – Yuzuriha Inori Dec 26 '19 at 11:47
  • $\begingroup$ It's up to you if you want to keep it, sometimes those duplicates are useful (it helps on searching), but since it has no answers you can freely delete it. $\endgroup$ – Zacky Dec 26 '19 at 11:56
  • $\begingroup$ Ah I see. Then let it be here. Thank you. $\endgroup$ – Yuzuriha Inori Dec 26 '19 at 11:57