What is the integral of sec (3x) tan (3x) dx?

∫tan^3(x)*sec^3(x) dx 

=∫tan^2(x)*sec^2(x)*(tanx*secx) dx 

=∫(sec^2(x) - 1)*sec^2(x)*(tanx*secx) dx 

=∫(sec^4(x) - sec^2(x))*(tanx*secx) dx 

=∫(sec^4(x)*(tanx*secx) dx - ∫sec^2(x))*(tanx*secx) dx 

=∫(sec^4(x)*d(secx) - ∫sec^2(x))d(secx) 

=(1/5)sec^5(x) - (1/3)sec^3(x) + c
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