Optimal. Leaf size=23 \[ 3 \left (e^{20-8 x+4 x \left (8-x^4\right )}-x\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 18, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {6706} \begin {gather*} 3 e^{-4 x^5+24 x+20}-3 x \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-3 x+\int e^{20+24 x-4 x^5} \left (72-60 x^4\right ) \, dx\\ &=3 e^{20+24 x-4 x^5}-3 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 18, normalized size = 0.78 \begin {gather*} 3 e^{20+24 x-4 x^5}-3 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 17, normalized size = 0.74 \begin {gather*} -3 \, x + 3 \, e^{\left (-4 \, x^{5} + 24 \, x + 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 17, normalized size = 0.74 \begin {gather*} -3 \, x + 3 \, e^{\left (-4 \, x^{5} + 24 \, x + 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 20, normalized size = 0.87
method | result | size |
default | \(-3 x +3 \,{\mathrm e}^{-4 x^{5}+24 x +20}\) | \(20\) |
norman | \(-3 x +3 \,{\mathrm e}^{-4 x^{5}+24 x +20}\) | \(20\) |
risch | \(-3 x +3 \,{\mathrm e}^{-4 \left (x +1\right ) \left (x^{4}-x^{3}+x^{2}-x -5\right )}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 17, normalized size = 0.74 \begin {gather*} -3 \, x + 3 \, e^{\left (-4 \, x^{5} + 24 \, x + 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.29, size = 18, normalized size = 0.78 \begin {gather*} 3\,{\mathrm {e}}^{24\,x}\,{\mathrm {e}}^{20}\,{\mathrm {e}}^{-4\,x^5}-3\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 15, normalized size = 0.65 \begin {gather*} - 3 x + 3 e^{- 4 x^{5} + 24 x + 20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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