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Today's calculation of Integral 748

Source: 2011 Hirosaki University entrance exam

August 30, 2011
calculusintegrationtrigonometrylogarithmscalculus computations

Problem Statement

Evaluate the following integrals.
(1) ∫0πcos⁡mxcos⁡nx dx (m, n=1, 2, ⋯ ).\int_0^{\pi} \cos mx\cos nx\ dx\ (m,\ n=1,\ 2,\ \cdots).
(2) ∫13(x−1x)(ln⁡x)2dx.\int_1^3 \left(x-\frac{1}{x}\right)(\ln x)^2dx.
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