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Math Help - evaluating the integral - and there is an e

  1. #1
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    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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  2. #2
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    Quote Originally Posted by calcbeg View Post
    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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