Complex Analysis: Theory and Applications · Problem 8.6.17

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · contour-integrals-residues

Problem

Use residues to compute the following integral: P.V.∫0∞ln⁡(1+x)x1+a dx,where 0<a<1.\text{P.V.} \int_0^\infty \frac{\ln(1+x)}{x^{1+a}} \, dx, \quad \text{where } 0 < a < 1.

Related theory

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