（a）令x=tant dx=sec^2tdt原式=∫(π/4,arctan2) sec^2tdt/tan^2tsect=∫(π/4,arctan2) costdt/sin^2t=∫(π/4,arctan2) d(sint)/sin^2t=-csct |(π/4,arctan2)=√2-√5/2（b）原式=∫ [(4-(x-2)^2]^(-3/2)dx令x...
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（a）令x=tant dx=sec^2tdt原式=∫(π/4,arctan2) sec^2tdt/tan^2tsect=∫(π/4,arctan2) costdt/sin^2t=∫(π/4,arctan2) d(sint)/sin^2t=-csct |(π/4,arctan2)=√2-√5/2（b）原式=∫ [(4-(x-2)^2]^(-3/2)dx令x...