- #1
ritwik06
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Homework Statement
Integrate:
[tex]\frac{Log[1+x]}{1+x^{2}}[/tex]
Homework Equations
Integration by parts.
The Attempt at a Solution
This is what Mathematica shows on Integrating this function
0.5 I (Log[1 + x] (Log[(-(0.5) - I/2) (I + x)] - Log[1 - (0.5 - I/2) (1 + x)]) - PolyLog[2, (0.5 - I/2) (1 + x)] + PolyLog[2, (1/2 + I/2) (1 + x)])
Where I is the iota.
This question was given to me in my maths class. I wonder if I can first of all find such a lengthy expression on integrating that and after that converting it to a real valued function.
If the integration is easier than what I think. Please let me know how to get started.
I used integration by parts to get uptil here:
I=ln(1+x)ArcTan(x)- [tex]\int\frac{ArcTan(x)}{1+x}[/tex]