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Mathematics
OpenStudy (anonymous):

how do you find the integral of (e^2x) / (1+(e^2x))^2 ?

OpenStudy (anonymous):

\[\int\limits \frac{e^{2 x}}{\left(1+e^{2 x}\right)^2} \, dx=-\frac{1}{2 \left(1+e^{2 x}\right)}+c \]

OpenStudy (anonymous):

i got an extra (1+e^2x) on the denominator...

OpenStudy (anonymous):

use u substitution. let u = 1+ e^2x ---> du= 2e^2xdx or 1/2du = e^2xdx

OpenStudy (anonymous):

then you have the integral of 1/u^2

OpenStudy (anonymous):

or 1/2 times that integral

OpenStudy (anonymous):

i used the formula for (u^n+1) / (n+1) + c .... did i use the formula correctly?

OpenStudy (anonymous):

once you do the substitution then yes

OpenStudy (anonymous):

oh! now i get what i did wrong....

OpenStudy (anonymous):

int[u^(-2)] is -u^(-1)

OpenStudy (anonymous):

thanks!

OpenStudy (anonymous):

no prob