Integrating [e^x / (1 + e^2x ) ]dx

  • Thread starter teng125
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  • #1
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integ [e^x / (1 + e^2x ) ]dx.can someone show me how to solve this by using 1 / (1 + x^2 ) formula??
pls.........
 

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  • #2
arildno
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What have you done?
 
  • #3
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i think of arranging it to be [e^x / (1 + {e^x}^2 ) ] but cannot related it to 1 / 1 + x^2
 
  • #4
arildno
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Good move! :smile:
Now, is it a clever change of variables that leaps into your eyes?
 
  • #5
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for the differentiation arctan x result is 1 / 1 + x^2 but for this ques how about the e^x on the numerator??
 
  • #6
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HINT: You can "get rid" of the [tex]e^x[/tex] in the numerator by a simple change of variables.
 
  • #7
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is it just subs e^x by u then diff du = e^x dx ??
 
  • #8
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Yes, that is correct. :smile:
 

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