Optimal. Leaf size=28 \[ e^{2 e^{e^{5+x^2}-x} x}+\left (-2+e^x\right ) x^3 \]
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Rubi [F] time = 1.08, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \left (-6 x^2+e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right )+e^x \left (3 x^2+x^3\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-2 x^3+\int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right ) \, dx+\int e^x \left (3 x^2+x^3\right ) \, dx\\ &=-2 x^3+\int e^x x^2 (3+x) \, dx+\int 2 e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (1-x+2 e^{5+x^2} x^2\right ) \, dx\\ &=-2 x^3+2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (1-x+2 e^{5+x^2} x^2\right ) \, dx+\int \left (3 e^x x^2+e^x x^3\right ) \, dx\\ &=-2 x^3+2 \int \left (e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x}-e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} x+2 e^{5+e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x+x^2} x^2\right ) \, dx+3 \int e^x x^2 \, dx+\int e^x x^3 \, dx\\ &=3 e^x x^2-2 x^3+e^x x^3+2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \, dx-2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} x \, dx-3 \int e^x x^2 \, dx+4 \int e^{5+e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x+x^2} x^2 \, dx-6 \int e^x x \, dx\\ &=-6 e^x x-2 x^3+e^x x^3+2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \, dx-2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} x \, dx+4 \int e^{5+e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x+x^2} x^2 \, dx+6 \int e^x \, dx+6 \int e^x x \, dx\\ &=6 e^x-2 x^3+e^x x^3+2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \, dx-2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} x \, dx+4 \int e^{5+e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x+x^2} x^2 \, dx-6 \int e^x \, dx\\ &=-2 x^3+e^x x^3+2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \, dx-2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} x \, dx+4 \int e^{5+e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x+x^2} x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.72, size = 31, normalized size = 1.11 \begin {gather*} e^{2 e^{e^{5+x^2}-x} x}-2 x^3+e^x x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.76, size = 62, normalized size = 2.21 \begin {gather*} {\left ({\left (x^{3} e^{x} - 2 \, x^{3}\right )} e^{\left (-x + e^{\left (x^{2} + 5\right )}\right )} + e^{\left (2 \, x e^{\left (-x + e^{\left (x^{2} + 5\right )}\right )} - x + e^{\left (x^{2} + 5\right )}\right )}\right )} e^{\left (x - e^{\left (x^{2} + 5\right )}\right )} \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*} \int -6 \, x^{2} + 2 \, {\left (2 \, x^{2} e^{\left (x^{2} + 5\right )} - x + 1\right )} e^{\left (2 \, x e^{\left (-x + e^{\left (x^{2} + 5\right )}\right )} - x + e^{\left (x^{2} + 5\right )}\right )} + {\left (x^{3} + 3 \, x^{2}\right )} e^{x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 28, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{x} x^{3}+{\mathrm e}^{2 x \,{\mathrm e}^{{\mathrm e}^{x^{2}+5}-x}}-2 x^{3}\) | \(28\) |
default | \({\mathrm e}^{x} x^{3}+{\mathrm e}^{2 x \,{\mathrm e}^{{\mathrm e}^{5} {\mathrm e}^{x^{2}}-x}}-2 x^{3}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.38, size = 49, normalized size = 1.75 \begin {gather*} -2 \, x^{3} + {\left (x^{3} - 3 \, x^{2} + 6 \, x - 6\right )} e^{x} + 3 \, {\left (x^{2} - 2 \, x + 2\right )} e^{x} + e^{\left (2 \, x e^{\left (-x + e^{\left (x^{2} + 5\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.68, size = 28, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{2\,x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}\,{\mathrm {e}}^5}}+x^3\,{\mathrm {e}}^x-2\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.72, size = 27, normalized size = 0.96 \begin {gather*} x^{3} e^{x} - 2 x^{3} + e^{2 x e^{- x + e^{5} e^{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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