Optimal. Leaf size=30 \[ 2 e^{\left (-x+e^{\frac {1}{4} \left (5+e^{3+e^x}\right )} x+x^2\right )^2} \]
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Rubi [A]
time = 5.23, antiderivative size = 32, normalized size of antiderivative = 1.07, number of steps
used = 2, number of rules used = 2, integrand size = 150, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {6820, 6838}
\begin {gather*} 2 e^{\left (-x-e^{\frac {1}{4} \left (e^{e^x+3}+5\right )}+1\right )^2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 6820
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{x^2 \left (-1+e^{\frac {1}{4} \left (5+e^{3+e^x}\right )}+x\right )^2} \left (1-e^{\frac {1}{4} \left (5+e^{3+e^x}\right )}-x\right ) x \left (4-4 e^{\frac {1}{4} \left (5+e^{3+e^x}\right )}-8 x-e^{\frac {17}{4}+\frac {e^{3+e^x}}{4}+e^x+x} x\right ) \, dx\\ &=2 e^{\left (1-e^{\frac {1}{4} \left (5+e^{3+e^x}\right )}-x\right )^2 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.32, size = 28, normalized size = 0.93 \begin {gather*} 2 e^{x^2 \left (-1+e^{\frac {1}{4} \left (5+e^{3+e^x}\right )}+x\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(50\) vs.
\(2(24)=48\).
time = 0.61, size = 51, normalized size = 1.70
method | result | size |
risch | \(2 \,{\mathrm e}^{x^{2} \left (2 x \,{\mathrm e}^{\frac {{\mathrm e}^{3+{\mathrm e}^{x}}}{4}+\frac {5}{4}}+x^{2}+{\mathrm e}^{\frac {{\mathrm e}^{3+{\mathrm e}^{x}}}{2}+\frac {5}{2}}-2 \,{\mathrm e}^{\frac {{\mathrm e}^{3+{\mathrm e}^{x}}}{4}+\frac {5}{4}}-2 x +1\right )}\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 66 vs.
\(2 (24) = 48\).
time = 0.36, size = 66, normalized size = 2.20 \begin {gather*} 2 \, e^{\left (x^{4} - 2 \, x^{3} + x^{2} e^{\left (\frac {1}{2} \, {\left (e^{\left (x + e^{x} + 3\right )} + 5 \, e^{x}\right )} e^{\left (-x\right )}\right )} + x^{2} + 2 \, {\left (x^{3} - x^{2}\right )} e^{\left (\frac {1}{4} \, {\left (e^{\left (x + e^{x} + 3\right )} + 5 \, e^{x}\right )} e^{\left (-x\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 54 vs.
\(2 (24) = 48\).
time = 8.54, size = 54, normalized size = 1.80 \begin {gather*} 2 e^{x^{4} - 2 x^{3} + x^{2} e^{\frac {e^{e^{x} + 3}}{2} + \frac {5}{2}} + x^{2} + \left (2 x^{3} - 2 x^{2}\right ) e^{\frac {e^{e^{x} + 3}}{4} + \frac {5}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.00, size = 63, normalized size = 2.10 \begin {gather*} 2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{5/2}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^3}{2}}}\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^{5/4}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^3}{4}}}\,{\mathrm {e}}^{2\,x^3\,{\mathrm {e}}^{5/4}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^3}{4}}}\,{\mathrm {e}}^{-2\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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