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

teng125 · Feb 15, 2006

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

arildno · Feb 15, 2006

What have you done?

teng125 · Feb 15, 2006

i think of arranging it to be [e^x / (1 + {e^x}^2 ) ] but cannot related it to 1 / 1 + x^2

arildno · Feb 15, 2006

Good move!
Now, is it a clever change of variables that leaps into your eyes?

teng125 · Feb 15, 2006

for the differentiation arctan x result is 1 / 1 + x^2 but for this ques how about the e^x on the numerator??

assyrian_77 · Feb 15, 2006

HINT: You can "get rid" of the [tex]e^x[/tex] in the numerator by a simple change of variables.

teng125 · Feb 15, 2006

is it just subs e^x by u then diff du = e^x dx ??

assyrian_77 · Feb 15, 2006

Yes, that is correct.