Optimal. Leaf size=22 \[ \frac {e^{e^{-4+2 x}}}{5-x-4 x^2} \]
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Rubi [A]
time = 0.08, antiderivative size = 42, normalized size of antiderivative = 1.91, number of steps
used = 1, number of rules used = 1, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {2326}
\begin {gather*} \frac {e^{e^{2 x-4}} \left (-4 x^2-x+5\right )}{16 x^4+8 x^3-39 x^2-10 x+25} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{e^{-4+2 x}} \left (5-x-4 x^2\right )}{25-10 x-39 x^2+8 x^3+16 x^4}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 21, normalized size = 0.95 \begin {gather*} -\frac {e^{e^{-4+2 x}}}{-5+x+4 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.83, size = 20, normalized size = 0.91
method | result | size |
norman | \(-\frac {{\mathrm e}^{{\mathrm e}^{2 x -4}}}{4 x^{2}+x -5}\) | \(20\) |
risch | \(-\frac {{\mathrm e}^{{\mathrm e}^{2 x -4}}}{4 x^{2}+x -5}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 19, normalized size = 0.86 \begin {gather*} -\frac {e^{\left (e^{\left (2 \, x - 4\right )}\right )}}{4 \, x^{2} + x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 19, normalized size = 0.86 \begin {gather*} -\frac {e^{\left (e^{\left (2 \, x - 4\right )}\right )}}{4 \, x^{2} + x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 17, normalized size = 0.77 \begin {gather*} - \frac {e^{e^{2 x - 4}}}{4 x^{2} + x - 5} \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 = 4.20, size = 20, normalized size = 0.91 \begin {gather*} -\frac {{\mathrm {e}}^{{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-4}}}{4\,x^2+x-5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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