∫(secx)^3dx=?

∫(secx)^3dx=∫secxdtanx
=secxtanx-∫tanxdsecx
=secxtanx-∫(tanx)^2secxdx
=secxtanx-∫(sec^2x-1)secxdx
=secxtanx-∫sec^3xdx+∫secxdx
=secxtanx-∫sec^3xdx+ln丨secx+tanx丨
所以∫(secx)^3dx=1/2(secxtanx+ln丨secx+tanx丨)+c
1

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