Optimal. Leaf size=24 \[ e^{-x} x \left (-2 x+e^{-e^{9 x^4}} x\right ) \]
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Rubi [F]
time = 0.68, 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^{-e^{9 x^4}-x} \left (2 x-x^2-36 e^{9 x^4} x^5+e^{e^{9 x^4}} \left (-4 x+2 x^2\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 \left (2 e^{-e^{9 x^4}-x} x+2 e^{-x} (-2+x) x-e^{-e^{9 x^4}-x} x^2-36 e^{-e^{9 x^4}-x+9 x^4} x^5\right ) \, dx\\ &=2 \int e^{-e^{9 x^4}-x} x \, dx+2 \int e^{-x} (-2+x) x \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ &=2 \int e^{-e^{9 x^4}-x} x \, dx+2 \int \left (-2 e^{-x} x+e^{-x} x^2\right ) \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ &=2 \int e^{-e^{9 x^4}-x} x \, dx+2 \int e^{-x} x^2 \, dx-4 \int e^{-x} x \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ &=4 e^{-x} x-2 e^{-x} x^2+2 \int e^{-e^{9 x^4}-x} x \, dx-4 \int e^{-x} \, dx+4 \int e^{-x} x \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ &=4 e^{-x}-2 e^{-x} x^2+2 \int e^{-e^{9 x^4}-x} x \, dx+4 \int e^{-x} \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ &=-2 e^{-x} x^2+2 \int e^{-e^{9 x^4}-x} x \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.25, size = 33, normalized size = 1.38 \begin {gather*} -e^{-e^{9 x^4}-x} \left (-1+2 e^{e^{9 x^4}}\right ) x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 28, normalized size = 1.17
method | result | size |
risch | \(-2 x^{2} {\mathrm e}^{-x}+x^{2} {\mathrm e}^{-x -{\mathrm e}^{9 x^{4}}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 41, normalized size = 1.71 \begin {gather*} x^{2} e^{\left (-x - e^{\left (9 \, x^{4}\right )}\right )} - 2 \, {\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x\right )} + 4 \, {\left (x + 1\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 27, normalized size = 1.12 \begin {gather*} -2 \, x^{2} e^{\left (-x\right )} + x^{2} e^{\left (-x - e^{\left (9 \, x^{4}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 2.12, size = 22, normalized size = 0.92 \begin {gather*} - 2 x^{2} e^{- x} + x^{2} e^{- x} e^{- e^{9 x^{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 = 3.61, size = 27, normalized size = 1.12 \begin {gather*} x^2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-{\mathrm {e}}^{9\,x^4}}-2\,x^2\,{\mathrm {e}}^{-x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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