Indefinite integral of TaNx ^ 3 Ask (TaNx) ^ 3, not tan (x ^ 3)

=∫tanx(tan²x)dx
=∫tanx(sec²x-1)dx
=∫tanxsec²xdx-∫tanxdx
=∫tanxdtanx-∫(sinx/cosx)dx
=(tan²x)/2-∫-dcosx/cosx
=(tan²x)/2+ln|cosx|+C