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

[teng125]

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

 

[arildno]

What have you done?

 

[teng125]

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

 

[arildno]

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

 

[teng125]

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]

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

 

[teng125]

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

 

[assyrian_77]

Yes, that is correct.