求积分f【(tant)^2*sect】dt

求积分f【(tant)^2*sect】dt

解：∵sect tant dt =d(sect)

∴ ∫tan²tsect dt

=∫ tant d(sect)

又∵ tant =√sec²t-1

∴∫ tant d(sect)

= ∫√sec²t-1 d(sect)

=(sect)/2×√sec²t-1 − 1/2×In(sect + √sec²t-1) +c

=(sect)/2×tant − 1/2×In(sect + tant) +c

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