. Many methods needed Show that Vĩ In x dx = T in the lo (1 + x)² following steps. a. Integrate by parts with u = Vĩ In x. b. Change variables by letting y = 1/x. In x c. Show that JoV(1 + x) dk = - In x 00 dx (and that both integrals converge). Conclude that In x dr = 0. lo Vã(1 + x)' d. Evaluate the remaining integral using the change of variables z = Vĩ. (Source: Mathematics Magazine 59, 1, Feb 1986)

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