aaslkd aaslkd
  • 07-05-2017
  • Mathematics
contestada

How do I find this? ∫((e^x)/(2+e^x))dx

Respuesta :

vulgus523
vulgus523 vulgus523
  • 07-05-2017
use u-substitution where u = 2+e^x
and since the derivative of e^x is e^x,
du = e^x
so in terms of 'u' the integral is 
∫(1/u)du (since the contents of u are on the bottom and the contents of du are on top)

and the integral of 1/u = ln(u) + C, so put x back into the equation using u's value

ln(u) + C = ln(2+e^x) + C
(C doesn't change because it just represents an unknown constant)
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