Question

tantsin²t不定积分怎么算呢？

Answer 1

∫tantsin²tdt=-∫sin²t/cost d(cost)=-∫(1/cost - cost)d(cost) = - (ln|cost| - 1/2 * cos²t) + c
= 1/2 * cos²t - ln|cost| + c, 望采纳

Answer 2

∫ tant. (sint)^2 dt
=∫ [(sint)^3/cost] dt
=∫ [-(sint)^2/cost] dcost
=∫ [(cost)^2-1]/cost dcost
=∫ ( cost - 1/cost) dcost
=(1/2)(cost)^2- ln|cost| + C