如图所示
∫(tant)^2.sect dt
=∫tant dsect
=tant.sect - ∫ (sect)^3 dt
=tant.sect -[ (1/2)sect.tant + (1/2)∫ sect dt]
=(1/2)tant.sect -(1/2)∫ sect dt
consider
∫ (sect)^3 dt
=∫ sect dtant
=sect.tant - ∫ (tant)^2 .sect dt
=sect.tant - ∫ [(sect)^2-1] .sect dt
2∫ (sect)^3 dt = sect.tant + ∫ sect dt
∫ (sect)^3 dt = (1/2)sect.tant + (1/2)∫ sect dt
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