Optimal. Leaf size=13 \[ \frac {\text {Ei}\left (t^2+1\right )}{2 e} \]
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Rubi [A] time = 0.07, antiderivative size = 13, normalized size of antiderivative = 1.00, 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 2178
Rule 6715
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*}
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Mathematica [A] time = 0.02, size = 13, normalized size = 1.00 \[ \frac {\text {Ei}\left (t^2+1\right )}{2 e} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 10, normalized size = 0.77 \[ \frac {1}{2} \, {\rm Ei}\left (t^{2} + 1\right ) e^{\left (-1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 10, normalized size = 0.77 \[ \frac {1}{2} \, {\rm Ei}\left (t^{2} + 1\right ) e^{\left (-1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 14, normalized size = 1.08 \[ -\frac {{\mathrm e}^{-1} \Ei \left (1, -t^{2}-1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.79, size = 13, normalized size = 1.00 \[ -\frac {1}{2} \, e^{\left (-1\right )} E_{1}\left (-t^{2} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 10, normalized size = 0.77 \[ \frac {{\mathrm {e}}^{-1}\,\mathrm {ei}\left (t^2+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {t e^{t^{2}}}{t^{2} + 1}\, dt \]
Verification of antiderivative is not currently implemented for this CAS.
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