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If the power for tangent is odd and there is at least one secant
Save a sec(x)tan(x), and turn all remaining tan²(x) into sec²(x)-1, then set u= sec(x)
If the power for secant is even (at least 2) and tan is even
Then save one copy of sec²(x), then convert all other sec²(x) to tan²(x)+1. The do u= tan(x).
when root(a²-x²)
sub x with x= a sin theta
when root(a²+x²)
sub x with x= a tan theta
when root(x²-a²)
sub x with x = a sec theta