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Solve for the indefinite integral e^x/(1+e^(2x))
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\[\int\limits_{}^{}(e^x/(1+e ^{2x})dx \] let u = e^x, then du = e^x dx. And note e^(2x) = (e^x)^2, or with the substitution, u^2: \[= \int\limits_{}^{}(1/(1+u^2))du = \arctan(u) + C = \arctan(e^x) + C\]
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