Optimal. Leaf size=13 \[ \frac{\text{ExpIntegralEi}\left (t^2+1\right )}{2 e} \]
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Rubi [A] time = 0.0654647, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {6715, 2178} \[ \frac{\text{ExpIntegralEi}\left (t^2+1\right )}{2 e} \]
Antiderivative was successfully verified.
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Rule 6715
Rule 2178
Rubi steps
\begin{align*} \int \frac{e^{t^2} t}{1+t^2} \, dt &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{e^t}{1+t} \, dt,t,t^2\right )\\ &=\frac{\text{Ei}\left (1+t^2\right )}{2 e}\\ \end{align*}
Mathematica [A] time = 0.0183979, size = 13, normalized size = 1. \[ \frac{\text{ExpIntegralEi}\left (t^2+1\right )}{2 e} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 14, normalized size = 1.1 \begin{align*} -{\frac{{{\rm e}^{-1}}{\it Ei} \left ( 1,-{t}^{2}-1 \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.035, size = 18, normalized size = 1.38 \begin{align*} -\frac{1}{2} \, e^{\left (-1\right )} E_{1}\left (-t^{2} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.12247, size = 32, normalized size = 2.46 \begin{align*} \frac{1}{2} \,{\rm Ei}\left (t^{2} + 1\right ) e^{\left (-1\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{t e^{t^{2}}}{t^{2} + 1}\, dt \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12824, size = 14, normalized size = 1.08 \begin{align*} \frac{1}{2} \,{\rm Ei}\left (t^{2} + 1\right ) e^{\left (-1\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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