SymPy Gamma

SymPy:

integrate (exp (x)/(1+exp (2*x)))

$\int \frac{e^{x}}{e^{2 x} + 1}\, dx$

-I*log(exp(x) - I)/2 + I*log(exp(x) + I)/2

$- \frac{i \log{\left(e^{x} - i \right)}}{2} + \frac{i \log{\left(e^{x} + i \right)}}{2}$

integrate(exp(x)/(exp(2*x) + 1), x)

Plot:

plot(RootSum(4*_z**2 + 1, Lambda(_i, _i*log(2*_i + exp(x)))))

Roots:

solve(RootSum(4*_z**2 + 1, Lambda(_i, _i*log(2*_i + exp(x)))), x)

$x =$

diff(RootSum(4*_z**2 + 1, Lambda(_i, _i*log(2*_i + exp(x)))), x)

$\frac{d}{d x} \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + e^{x} \right)} \right)\right)} =$

series(RootSum(4*_z**2 + 1, Lambda(_i, _i*log(2*_i + exp(x)))), x, 0, 10)

See what Wolfram|Alpha has to say.

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