Optimal. Leaf size=34 \[ 3 e^{-\left (e^x-e^{2 \left (e^{4-e^{x^2}}+x\right )}\right )^4 x^2} \]
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Rubi [F] time = 47.45, 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 \exp \left (-e^{4 x} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2-e^{8 e^{4-e^{x^2}}+8 x} x^2\right ) \left (e^{4 x} \left (-6 x-12 x^2\right )+e^{8 e^{4-e^{x^2}}+8 x} \left (-6 x-24 x^2+48 e^{4-e^{x^2}+x^2} x^3\right )+e^{4 e^{4-e^{x^2}}+4 x} \left (144 e^{4-e^{x^2}+2 x+x^2} x^3+e^{2 x} \left (-36 x-108 x^2\right )\right )+e^{2 e^{4-e^{x^2}}+2 x} \left (-48 e^{4-e^{x^2}+3 x+x^2} x^3+e^{3 x} \left (24 x+60 x^2\right )\right )+e^{6 e^{4-e^{x^2}}+6 x} \left (-144 e^{4-e^{x^2}+x+x^2} x^3+e^x \left (24 x+84 x^2\right )\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int 6 \exp \left (-e^{x^2}+4 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2\right ) \left (1-e^{2 e^{4-e^{x^2}}+x}\right )^3 x \left (-8 e^{4+2 e^{4-e^{x^2}}+x+x^2} x^2-e^{e^{x^2}} (1+2 x)+e^{2 e^{4-e^{x^2}}+e^{x^2}+x} (1+4 x)\right ) \, dx\\ &=6 \int \exp \left (-e^{x^2}+4 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2\right ) \left (1-e^{2 e^{4-e^{x^2}}+x}\right )^3 x \left (-8 e^{4+2 e^{4-e^{x^2}}+x+x^2} x^2-e^{e^{x^2}} (1+2 x)+e^{2 e^{4-e^{x^2}}+e^{x^2}+x} (1+4 x)\right ) \, dx\\ &=6 \int \left (8 \exp \left (4+2 e^{4-e^{x^2}}-e^{x^2}+5 x+x^2-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2\right ) \left (-1+e^{2 e^{4-e^{x^2}}+x}\right )^3 x^3-\exp \left (4 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2\right ) \left (-1+e^{2 e^{4-e^{x^2}}+x}\right )^3 x \left (-1+e^{2 e^{4-e^{x^2}}+x}-2 x+4 e^{2 e^{4-e^{x^2}}+x} x\right )\right ) \, dx\\ &=-\left (6 \int \exp \left (4 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2\right ) \left (-1+e^{2 e^{4-e^{x^2}}+x}\right )^3 x \left (-1+e^{2 e^{4-e^{x^2}}+x}-2 x+4 e^{2 e^{4-e^{x^2}}+x} x\right ) \, dx\right )+48 \int \exp \left (4+2 e^{4-e^{x^2}}-e^{x^2}+5 x+x^2-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2\right ) \left (-1+e^{2 e^{4-e^{x^2}}+x}\right )^3 x^3 \, dx\\ &=-\left (6 \int \left (e^{4 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x (1+2 x)+6 e^{4 e^{4-e^{x^2}}+6 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x (1+3 x)+e^{8 e^{4-e^{x^2}}+8 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x (1+4 x)-2 e^{2 e^{4-e^{x^2}}+5 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x (2+5 x)-2 e^{6 e^{4-e^{x^2}}+7 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x (2+7 x)\right ) \, dx\right )+48 \int \left (-e^{4+2 e^{4-e^{x^2}}-e^{x^2}+5 x+x^2-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x^3+3 e^{4+4 e^{4-e^{x^2}}-e^{x^2}+6 x+x^2-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x^3-3 e^{4+6 e^{4-e^{x^2}}-e^{x^2}+7 x+x^2-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x^3+e^{4+8 e^{4-e^{x^2}}-e^{x^2}+8 x+x^2-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x^3\right ) \, dx\\ &=-\left (6 \int e^{4 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x (1+2 x) \, dx\right )-6 \int e^{8 e^{4-e^{x^2}}+8 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x (1+4 x) \, dx+12 \int e^{2 e^{4-e^{x^2}}+5 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x (2+5 x) \, dx+12 \int e^{6 e^{4-e^{x^2}}+7 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x (2+7 x) \, dx-36 \int e^{4 e^{4-e^{x^2}}+6 x-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x (1+3 x) \, dx-48 \int e^{4+2 e^{4-e^{x^2}}-e^{x^2}+5 x+x^2-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x^3 \, dx+48 \int e^{4+8 e^{4-e^{x^2}}-e^{x^2}+8 x+x^2-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x^3 \, dx+144 \int e^{4+4 e^{4-e^{x^2}}-e^{x^2}+6 x+x^2-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x^3 \, dx-144 \int e^{4+6 e^{4-e^{x^2}}-e^{x^2}+7 x+x^2-e^{4 x} x^2-e^{8 \left (e^{4-e^{x^2}}+x\right )} x^2+4 e^{2 e^{4-e^{x^2}}+5 x} x^2-6 e^{4 e^{4-e^{x^2}}+6 x} x^2+4 e^{6 e^{4-e^{x^2}}+7 x} x^2} x^3 \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.53, size = 35, normalized size = 1.03 \begin {gather*} 3 e^{-e^{4 x} \left (-1+e^{2 e^{4-e^{x^2}}+x}\right )^4 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.87, size = 216, normalized size = 6.35 \begin {gather*} 3 \, e^{\left (-{\left (x^{2} e^{\left (4 \, {\left (5 \, x e^{\left (x^{2} + 3 \, x\right )} + 2 \, e^{\left (x^{2} + 3 \, x - e^{\left (x^{2}\right )} + 4\right )}\right )} e^{\left (-x^{2} - 3 \, x\right )}\right )} - 4 \, x^{2} e^{\left (3 \, {\left (5 \, x e^{\left (x^{2} + 3 \, x\right )} + 2 \, e^{\left (x^{2} + 3 \, x - e^{\left (x^{2}\right )} + 4\right )}\right )} e^{\left (-x^{2} - 3 \, x\right )} + 4 \, x\right )} + 6 \, x^{2} e^{\left (2 \, {\left (5 \, x e^{\left (x^{2} + 3 \, x\right )} + 2 \, e^{\left (x^{2} + 3 \, x - e^{\left (x^{2}\right )} + 4\right )}\right )} e^{\left (-x^{2} - 3 \, x\right )} + 8 \, x\right )} - 4 \, x^{2} e^{\left ({\left (5 \, x e^{\left (x^{2} + 3 \, x\right )} + 2 \, e^{\left (x^{2} + 3 \, x - e^{\left (x^{2}\right )} + 4\right )}\right )} e^{\left (-x^{2} - 3 \, x\right )} + 12 \, x\right )} + x^{2} e^{\left (16 \, x\right )}\right )} e^{\left (-12 \, x\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 \, {\left ({\left (2 \, x^{2} + x\right )} e^{\left (4 \, x\right )} - {\left (8 \, x^{3} e^{\left (x^{2} - e^{\left (x^{2}\right )} + 4\right )} - 4 \, x^{2} - x\right )} e^{\left (8 \, x + 8 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )} + 2 \, {\left (12 \, x^{3} e^{\left (x^{2} + x - e^{\left (x^{2}\right )} + 4\right )} - {\left (7 \, x^{2} + 2 \, x\right )} e^{x}\right )} e^{\left (6 \, x + 6 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )} - 6 \, {\left (4 \, x^{3} e^{\left (x^{2} + 2 \, x - e^{\left (x^{2}\right )} + 4\right )} - {\left (3 \, x^{2} + x\right )} e^{\left (2 \, x\right )}\right )} e^{\left (4 \, x + 4 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )} + 2 \, {\left (4 \, x^{3} e^{\left (x^{2} + 3 \, x - e^{\left (x^{2}\right )} + 4\right )} - {\left (5 \, x^{2} + 2 \, x\right )} e^{\left (3 \, x\right )}\right )} e^{\left (2 \, x + 2 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )}\right )} e^{\left (-x^{2} e^{\left (4 \, x\right )} - x^{2} e^{\left (8 \, x + 8 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )} + 4 \, x^{2} e^{\left (7 \, x + 6 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )} - 6 \, x^{2} e^{\left (6 \, x + 4 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )} + 4 \, x^{2} e^{\left (5 \, x + 2 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.20, size = 84, normalized size = 2.47
method | result | size |
risch | \(3 \,{\mathrm e}^{-x^{2} \left ({\mathrm e}^{8 \,{\mathrm e}^{4-{\mathrm e}^{x^{2}}}+8 x}+{\mathrm e}^{4 x}-4 \,{\mathrm e}^{7 x +6 \,{\mathrm e}^{4-{\mathrm e}^{x^{2}}}}+6 \,{\mathrm e}^{6 x +4 \,{\mathrm e}^{4-{\mathrm e}^{x^{2}}}}-4 \,{\mathrm e}^{5 x +2 \,{\mathrm e}^{4-{\mathrm e}^{x^{2}}}}\right )}\) | \(84\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.07, size = 97, normalized size = 2.85 \begin {gather*} 3 \, e^{\left (-x^{2} e^{\left (4 \, x\right )} - x^{2} e^{\left (8 \, x + 8 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )} + 4 \, x^{2} e^{\left (7 \, x + 6 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )} - 6 \, x^{2} e^{\left (6 \, x + 4 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )} + 4 \, x^{2} e^{\left (5 \, x + 2 \, e^{\left (-e^{\left (x^{2}\right )} + 4\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.86, size = 100, normalized size = 2.94 \begin {gather*} 3\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^{-{\mathrm {e}}^{x^2}}\,{\mathrm {e}}^4}\,{\mathrm {e}}^{5\,x}}\,{\mathrm {e}}^{-6\,x^2\,{\mathrm {e}}^{4\,{\mathrm {e}}^{-{\mathrm {e}}^{x^2}}\,{\mathrm {e}}^4}\,{\mathrm {e}}^{6\,x}}\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^{6\,{\mathrm {e}}^{-{\mathrm {e}}^{x^2}}\,{\mathrm {e}}^4}\,{\mathrm {e}}^{7\,x}}\,{\mathrm {e}}^{-x^2\,{\mathrm {e}}^{8\,{\mathrm {e}}^{-{\mathrm {e}}^{x^2}}\,{\mathrm {e}}^4}\,{\mathrm {e}}^{8\,x}}\,{\mathrm {e}}^{-x^2\,{\mathrm {e}}^{4\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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