Optimal. Leaf size=21 \[ e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x^2 \]
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Rubi [F] time = 6.07, 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 e^{58 x+60 x^2-2 e^{e^{-2 x}} \left (x+x^2\right )} \left (e^{2 x} \left (2 x+60 x^2+120 x^3\right )+e^{e^{-2 x}} \left (4 x^3+4 x^4+e^{2 x} \left (-2 x^2-4 x^3\right )\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \exp \left (-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) \left (e^{2 x} \left (2 x+60 x^2+120 x^3\right )+e^{e^{-2 x}} \left (4 x^3+4 x^4+e^{2 x} \left (-2 x^2-4 x^3\right )\right )\right ) \, dx\\ &=\int \left (2 \exp \left (e^{-2 x}-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^2 \left (-e^{2 x}+2 x-2 e^{2 x} x+2 x^2\right )+2 \exp \left (2 x-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x \left (1+30 x+60 x^2\right )\right ) \, dx\\ &=2 \int \exp \left (e^{-2 x}-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^2 \left (-e^{2 x}+2 x-2 e^{2 x} x+2 x^2\right ) \, dx+2 \int \exp \left (2 x-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x \left (1+30 x+60 x^2\right ) \, dx\\ &=2 \int e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x \left (1+30 x+60 x^2\right ) \, dx+2 \int \left (2 \exp \left (e^{-2 x}-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^3 (1+x)-\exp \left (e^{-2 x}+2 x-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^2 (1+2 x)\right ) \, dx\\ &=-\left (2 \int \exp \left (e^{-2 x}+2 x-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^2 (1+2 x) \, dx\right )+2 \int \left (e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x+30 e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x^2+60 e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x^3\right ) \, dx+4 \int \exp \left (e^{-2 x}-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^3 (1+x) \, dx\\ &=2 \int e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x \, dx-2 \int \left (\exp \left (e^{-2 x}+2 x-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^2+2 \exp \left (e^{-2 x}+2 x-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^3\right ) \, dx+4 \int \left (\exp \left (e^{-2 x}-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^3+\exp \left (e^{-2 x}-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^4\right ) \, dx+60 \int e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x^2 \, dx+120 \int e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x^3 \, dx\\ &=2 \int e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x \, dx-2 \int \exp \left (e^{-2 x}+2 x-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^2 \, dx+4 \int \exp \left (e^{-2 x}-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^3 \, dx-4 \int \exp \left (e^{-2 x}+2 x-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^3 \, dx+4 \int \exp \left (e^{-2 x}-2 x \left (-29+e^{e^{-2 x}}-30 x+e^{e^{-2 x}} x\right )\right ) x^4 \, dx+60 \int e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x^2 \, dx+120 \int e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x^3 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.82, size = 21, normalized size = 1.00 \begin {gather*} e^{-2 \left (-30+e^{e^{-2 x}}\right ) x (1+x)} x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 26, normalized size = 1.24 \begin {gather*} x^{2} e^{\left (60 \, x^{2} - 2 \, {\left (x^{2} + x\right )} e^{\left (e^{\left (-2 \, x\right )}\right )} + 60 \, x\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 2 \, {\left ({\left (60 \, x^{3} + 30 \, x^{2} + x\right )} e^{\left (2 \, x\right )} + {\left (2 \, x^{4} + 2 \, x^{3} - {\left (2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x\right )}\right )} e^{\left (e^{\left (-2 \, x\right )}\right )}\right )} e^{\left (60 \, x^{2} - 2 \, {\left (x^{2} + x\right )} e^{\left (e^{\left (-2 \, x\right )}\right )} + 58 \, x\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 19, normalized size = 0.90
method | result | size |
risch | \(x^{2} {\mathrm e}^{-2 x \left (x +1\right ) \left ({\mathrm e}^{{\mathrm e}^{-2 x}}-30\right )}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 32, normalized size = 1.52 \begin {gather*} x^{2} e^{\left (-2 \, x^{2} e^{\left (e^{\left (-2 \, x\right )}\right )} + 60 \, x^{2} - 2 \, x e^{\left (e^{\left (-2 \, x\right )}\right )} + 60 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.83, size = 34, normalized size = 1.62 \begin {gather*} x^2\,{\mathrm {e}}^{60\,x}\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^{-2\,x}}}\,{\mathrm {e}}^{60\,x^2}\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^{{\mathrm {e}}^{-2\,x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.96, size = 27, normalized size = 1.29 \begin {gather*} x^{2} e^{60 x^{2} + 60 x - 2 \left (x^{2} + x\right ) e^{e^{- 2 x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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