为什么 ∫ sec^2dt=ln|sect+tant|+c?

为什么 ∫ sec^2dt=ln|sect+tant|+c?

题目写错了,∫ sec²t dt = tant + C
而∫ sect dt
= ∫ sect * (sect + tant)/(sect + tant) dt
= ∫ (secttant + sec²t)/(sect + tant) dt
= ∫ 1/(sect + tant) d(sect + tant)
= ln|sect + tant| + C