Optimal. Leaf size=23 \[ \frac {4 e^{5+x-(3-x) x-4 x^3}}{x} \]
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Rubi [A] time = 0.07, antiderivative size = 44, normalized size of antiderivative = 1.91, number of steps used = 1, number of rules used = 1, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {2288} \begin {gather*} \frac {4 e^{-4 x^3+x^2-2 x+5} \left (6 x^3-x^2+x\right )}{x^2 \left (6 x^2-x+1\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {4 e^{5-2 x+x^2-4 x^3} \left (x-x^2+6 x^3\right )}{x^2 \left (1-x+6 x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 20, normalized size = 0.87 \begin {gather*} \frac {4 e^{5-2 x+x^2-4 x^3}}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 19, normalized size = 0.83 \begin {gather*} \frac {4 \, e^{\left (-4 \, x^{3} + x^{2} - 2 \, x + 5\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 19, normalized size = 0.83 \begin {gather*} \frac {4 \, e^{\left (-4 \, x^{3} + x^{2} - 2 \, x + 5\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 22, normalized size = 0.96
method | result | size |
risch | \(\frac {4 \,{\mathrm e}^{-\left (x -1\right ) \left (4 x^{2}+3 x +5\right )}}{x}\) | \(22\) |
gosper | \(\frac {4 \,{\mathrm e}^{5} {\mathrm e}^{-4 x^{3}} {\mathrm e}^{x^{2}-2 x}}{x}\) | \(28\) |
norman | \(\frac {4 \,{\mathrm e}^{5} {\mathrm e}^{-4 x^{3}} {\mathrm e}^{x^{2}-2 x}}{x}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 19, normalized size = 0.83 \begin {gather*} \frac {4 \, e^{\left (-4 \, x^{3} + x^{2} - 2 \, x + 5\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.50, size = 21, normalized size = 0.91 \begin {gather*} \frac {4\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^5\,{\mathrm {e}}^{-4\,x^3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 20, normalized size = 0.87 \begin {gather*} \frac {4 e^{5} e^{- 4 x^{3}} e^{x^{2} - 2 x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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