Optimal. Leaf size=23 \[ \frac {e^{1+e^{1+x}-x+\frac {x^4}{9}}}{x^4} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(58\) vs. \(2(23)=46\).
time = 0.15, antiderivative size = 58, normalized size of antiderivative = 2.52, number of steps
used = 2, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 2326}
\begin {gather*} \frac {e^{\frac {1}{9} \left (x^4-9 x+9 e^{x+1}+9\right )} \left (-4 x^4-9 e^{x+1} x+9 x\right )}{x^5 \left (-4 x^3-9 e^{x+1}+9\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \frac {e^{\frac {1}{9} \left (9+9 e^{1+x}-9 x+x^4\right )} \left (-36-9 x+9 e^{1+x} x+4 x^4\right )}{x^5} \, dx\\ &=\frac {e^{\frac {1}{9} \left (9+9 e^{1+x}-9 x+x^4\right )} \left (9 x-9 e^{1+x} x-4 x^4\right )}{x^5 \left (9-9 e^{1+x}-4 x^3\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 23, normalized size = 1.00 \begin {gather*} \frac {e^{1+e^{1+x}-x+\frac {x^4}{9}}}{x^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.52, size = 20, normalized size = 0.87
method | result | size |
risch | \(\frac {{\mathrm e}^{{\mathrm e}^{x +1}+\frac {x^{4}}{9}-x +1}}{x^{4}}\) | \(20\) |
norman | \(\frac {{\mathrm e}^{{\mathrm e} \,{\mathrm e}^{x}+\frac {x^{4}}{9}-x +1}}{x^{4}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 19, normalized size = 0.83 \begin {gather*} \frac {e^{\left (\frac {1}{9} \, x^{4} - x + e^{\left (x + 1\right )} + 1\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 19, normalized size = 0.83 \begin {gather*} \frac {e^{\left (\frac {1}{9} \, x^{4} - x + e^{\left (x + 1\right )} + 1\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 19, normalized size = 0.83 \begin {gather*} \frac {e^{\frac {x^{4}}{9} - x + e e^{x} + 1}}{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 = 4.83, size = 22, normalized size = 0.96 \begin {gather*} \frac {{\mathrm {e}}^{\mathrm {e}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-x}\,\mathrm {e}\,{\mathrm {e}}^{\frac {x^4}{9}}}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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