Compute the following integrals.

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Compute the following integrals. (1) (i)∫0∞f(xn+x−n)ln⁡xdxx=0(i) \int_0^\infty f(x^n + x^{-n}) \ln x \frac{dx}{x} = 0 (2) (ii)∫0∞f(xn+x−n)ln⁡xdx1+x2=0(ii) \int_0^\infty f(x^n + x^{-n}) \ln x \frac{dx}{1+x^2} = 0

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