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PutnamSuperchallengeIntegrals I: Feynman's Trick

Integrals I: Feynman's Trick · Superchallenge problem

Evaluate ∫0∞ln⁡(1+12x2)1+x2 dx\displaystyle\int_0^{\infty} \frac{\ln\left(1 + 1^2x^2\right)}{1 + x^2}\,dx.