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OpenStudy (anonymous):
how do you find the integral of (e^2x) / (1+(e^2x))^2 ?
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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
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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!
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OpenStudy (anonymous):
no prob
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