Optimal. Leaf size=32 \[ e^{e^{(3+x)^4} x} (-x+(4-x) (2+2 x))-\log (5) \]
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Rubi [B] time = 0.25, antiderivative size = 132, normalized size of antiderivative = 4.12, number of steps used = 2, number of rules used = 2, integrand size = 103, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {1586, 2288} \begin {gather*} \frac {\left (-8 x^6-52 x^5-4 x^4+612 x^3+1402 x^2+869 x+8\right ) \exp \left (x^4+12 x^3+54 x^2+e^{x^4+12 x^3+54 x^2+108 x+81} x+108 x+81\right )}{4 e^{x^4+12 x^3+54 x^2+108 x+81} x \left (x^3+9 x^2+27 x+27\right )+e^{x^4+12 x^3+54 x^2+108 x+81}} \end {gather*}
Antiderivative was successfully verified.
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Rule 1586
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\int e^{e^{81+108 x+54 x^2+12 x^3+x^4} x} \left (-5+4 x+e^{81+108 x+54 x^2+12 x^3+x^4} \left (-8-869 x-1402 x^2-612 x^3+4 x^4+52 x^5+8 x^6\right )\right ) \, dx\\ &=\frac {\exp \left (81+108 x+e^{81+108 x+54 x^2+12 x^3+x^4} x+54 x^2+12 x^3+x^4\right ) \left (8+869 x+1402 x^2+612 x^3-4 x^4-52 x^5-8 x^6\right )}{e^{81+108 x+54 x^2+12 x^3+x^4}+4 e^{81+108 x+54 x^2+12 x^3+x^4} x \left (27+27 x+9 x^2+x^3\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.14, size = 22, normalized size = 0.69 \begin {gather*} e^{e^{(3+x)^4} x} \left (8+5 x-2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 34, normalized size = 1.06 \begin {gather*} e^{\left (x e^{\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )} + \log \left (-2 \, x^{2} + 5 \, x + 8\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.51, size = 34, normalized size = 1.06 \begin {gather*} e^{\left (x e^{\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )} + \log \left (-2 \, x^{2} + 5 \, x + 8\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.46, size = 21, normalized size = 0.66
method | result | size |
risch | \(\left (-2 x^{2}+5 x +8\right ) {\mathrm e}^{{\mathrm e}^{\left (3+x \right )^{4}} x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.91, size = 34, normalized size = 1.06 \begin {gather*} -{\left (2 \, x^{2} - 5 \, x - 8\right )} e^{\left (x e^{\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.24, size = 36, normalized size = 1.12 \begin {gather*} {\mathrm {e}}^{x\,{\mathrm {e}}^{108\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{81}\,{\mathrm {e}}^{12\,x^3}\,{\mathrm {e}}^{54\,x^2}}\,\left (-2\,x^2+5\,x+8\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 6.00, size = 32, normalized size = 1.00 \begin {gather*} \left (- 2 x^{2} + 5 x + 8\right ) e^{x e^{x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 81}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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