evaluating the integral - and there is an e

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?

Thanks

Calculus Beginner

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Originally Posted by calcbeg

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 ... 3^x or e^x in the numerator ?

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

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