Hi I will just preamble this with - "I have developed a strong hatred for the letter e"
So the integral is integral sign ("S") 3^x/(sqrt(e^2x +1)) dx
so if I let U = e^x then x = ln u (I found this in another solution) then dx = du/u
so S (e^x)/(sqrt (e^2x +1)) dx = S u/sqrt(u^2 +1) (du/u)
= S du/ sqrt (u^2 +1)
= sqrt(u^2 + 1) (2u) + C
=2e^x (sqrt(e^2x + 1) +C
Did I do this correctly?