Optimal. Leaf size=4 \[ e^{\tan ^{-1}(x)} \]
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Rubi [A] time = 0.0205325, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {5071} \[ e^{\tan ^{-1}(x)} \]
Antiderivative was successfully verified.
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Rule 5071
Rubi steps
\begin{align*} \int \frac{e^{\tan ^{-1}(x)}}{1+x^2} \, dx &=e^{\tan ^{-1}(x)}\\ \end{align*}
Mathematica [C] time = 0.0042299, size = 27, normalized size = 6.75 \[ (1-i x)^{\frac{i}{2}} (1+i x)^{-\frac{i}{2}} \]
Warning: Unable to verify antiderivative.
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Maple [A] time = 0.003, size = 4, normalized size = 1. \begin{align*}{{\rm e}^{\arctan \left ( x \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.925476, size = 4, normalized size = 1. \begin{align*} e^{\arctan \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.18507, size = 18, normalized size = 4.5 \begin{align*} e^{\arctan \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.866199, size = 3, normalized size = 0.75 \begin{align*} e^{\operatorname{atan}{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04797, size = 4, normalized size = 1. \begin{align*} e^{\arctan \left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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