(a) Show that the integral 0(1/x) sin x dx converges. (b) Show that 2 (1/ln x sin...

(a) Show that the integral ˆ«ˆž0(1/x) sin x dx converges.
(b) Show that ˆ«ˆž2 (1/ln xÞ sin x dx converges.
(c) Show that ˆ«ˆž0 (1/ˆšx) cos x dx converges.
(d) Show that the Chartier-Dirichlet Test does not apply to establish the convergence of ˆ«ˆž0(x/(x + 1)) sin(x2)dx by taking f(x) := sin(x2).

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lim φ(x)