Can some one help me evaluate the integral ?

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Can some one help me evaluate the integral ?

Mathematics
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\[\int\limits e^x/(1+e^{2x}) dx\]
I thought the answer should be arctan(e^x) +c but somehow the answer tells me that there is a 1/2 multiplied to it. I can't figure out where it got that from.
\[\int\limits \frac{e^x}{1+e^{2x}} dx\]\[= \int\limits \frac{e^x}{1+(e^x)^2} dx\] let u = e^x and solve, how come? I got arcTan(e^x) too

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Other answers:

1/2 can come from \[u=e ^{2x}\]

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