Optimal. Leaf size=15 \[ e^{20 e^{-2 x+9 x^3}} \]
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Rubi [F]
time = 0.26, 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^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\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 (-40 e^{20 e^{-2 x+9 x^3}-2 x+9 x^3}+540 e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} x^2\right ) \, dx\\ &=-\left (40 \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \, dx\right )+540 \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 15, normalized size = 1.00 \begin {gather*} e^{20 e^{-2 x+9 x^3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 14, normalized size = 0.93
method | result | size |
risch | \({\mathrm e}^{20 \,{\mathrm e}^{x \left (9 x^{2}-2\right )}}\) | \(14\) |
norman | \({\mathrm e}^{20 \,{\mathrm e}^{9 x^{3}-2 x}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.38, size = 13, normalized size = 0.87 \begin {gather*} e^{\left (20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 13, normalized size = 0.87 \begin {gather*} e^{\left (20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 12, normalized size = 0.80 \begin {gather*} e^{20 e^{9 x^{3} - 2 x}} \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 = 0.10, size = 13, normalized size = 0.87 \begin {gather*} {\mathrm {e}}^{20\,{\mathrm {e}}^{9\,x^3-2\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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