Optimal. Leaf size=12 \[ e^{\left (22+e^3+x\right )^2}+x \]
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Rubi [A] time = 0.09, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {2227, 2209} \begin {gather*} x+e^{\left (x+e^3+22\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+\int e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right ) \, dx\\ &=x+\int e^{\left (22+e^3+x\right )^2} \left (44+2 e^3+2 x\right ) \, dx\\ &=e^{\left (22+e^3+x\right )^2}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} e^{\left (22+e^3+x\right )^2}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.48, size = 20, normalized size = 1.67 \begin {gather*} x + e^{\left (x^{2} + 2 \, {\left (x + 22\right )} e^{3} + 44 \, x + e^{6} + 484\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.58, size = 22, normalized size = 1.83 \begin {gather*} x + e^{\left (x^{2} + 2 \, x e^{3} + 44 \, x + e^{6} + 44 \, e^{3} + 484\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 23, normalized size = 1.92
method | result | size |
risch | \(x +{\mathrm e}^{2 x \,{\mathrm e}^{3}+x^{2}+44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+44 x +484}\) | \(23\) |
norman | \(x +{\mathrm e}^{{\mathrm e}^{6}+\left (2 x +44\right ) {\mathrm e}^{3}+x^{2}+44 x +484}\) | \(24\) |
default | \(x +{\mathrm e}^{x^{2}+\left (2 \,{\mathrm e}^{3}+44\right ) x +44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+484}+\frac {i \left (2 \,{\mathrm e}^{3}+44\right ) \sqrt {\pi }\, {\mathrm e}^{44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+484-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \erf \left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )}{2}-i \sqrt {\pi }\, {\mathrm e}^{44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+487-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \erf \left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )-22 i \sqrt {\pi }\, {\mathrm e}^{44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+484-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \erf \left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )\) | \(149\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 20, normalized size = 1.67 \begin {gather*} x + e^{\left (x^{2} + 2 \, {\left (x + 22\right )} e^{3} + 44 \, x + e^{6} + 484\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 27, normalized size = 2.25 \begin {gather*} x+{\mathrm {e}}^{44\,{\mathrm {e}}^3}\,{\mathrm {e}}^{44\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{484}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^3}\,{\mathrm {e}}^{{\mathrm {e}}^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.11, size = 22, normalized size = 1.83 \begin {gather*} x + e^{x^{2} + 44 x + \left (2 x + 44\right ) e^{3} + e^{6} + 484} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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