how do I find integral of 3^tgx(tg^2x+1)

Answer 1

We can rewrite this as f(x) = e^(tgx ln(3)) (e^(2x ln(tg)) + 1) =

e^((tg ln(3) + 2 ln(tg))x) + e^(tg ln(3) x )

Thus, the integral is 1/((tg ln(3) + 2 ln(tg)) 3^tgx tg^2x + 1/(tg ln(3)) 3^tgx + C