Optimal. Leaf size=22 \[ \frac {4-12 e^{e^{\frac {e^x}{12}}+x} x}{x} \]
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Rubi [F]
time = 0.06, 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 \frac {-4+e^{e^{\frac {e^x}{12}}+x} \left (-12 x^2-e^{\frac {e^x}{12}+x} x^2\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-12 e^{e^{\frac {e^x}{12}}+x}-e^{\frac {1}{12} \left (12 e^{\frac {e^x}{12}}+e^x+24 x\right )}-\frac {4}{x^2}\right ) \, dx\\ &=\frac {4}{x}-12 \int e^{e^{\frac {e^x}{12}}+x} \, dx-\int e^{\frac {1}{12} \left (12 e^{\frac {e^x}{12}}+e^x+24 x\right )} \, dx\\ &=\frac {4}{x}-12 \text {Subst}\left (\int e^{e^{x/12}} \, dx,x,e^x\right )-\int e^{\frac {1}{12} \left (12 e^{\frac {e^x}{12}}+e^x+24 x\right )} \, dx\\ &=\frac {4}{x}-144 \text {Subst}\left (\int \frac {e^x}{x} \, dx,x,e^{\frac {e^x}{12}}\right )-\int e^{\frac {1}{12} \left (12 e^{\frac {e^x}{12}}+e^x+24 x\right )} \, dx\\ &=\frac {4}{x}-144 \text {Ei}\left (e^{\frac {e^x}{12}}\right )-\int e^{\frac {1}{12} \left (12 e^{\frac {e^x}{12}}+e^x+24 x\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 21, normalized size = 0.95 \begin {gather*} -12 e^{e^{\frac {e^x}{12}}+x}+\frac {4}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 17, normalized size = 0.77
method | result | size |
risch | \(\frac {4}{x}-12 \,{\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{x}}{12}}+x}\) | \(17\) |
norman | \(\frac {4-12 x \,{\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{x}}{12}}+x}}{x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 16, normalized size = 0.73 \begin {gather*} \frac {4}{x} - 12 \, e^{\left (x + e^{\left (\frac {1}{12} \, e^{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 28, normalized size = 1.27 \begin {gather*} -\frac {4 \, {\left (3 \, x e^{\left ({\left (x e^{x} + e^{\left (x + \frac {1}{12} \, e^{x}\right )}\right )} e^{\left (-x\right )}\right )} - 1\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 14, normalized size = 0.64 \begin {gather*} - 12 e^{x + e^{\frac {e^{x}}{12}}} + \frac {4}{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 = 16, normalized size = 0.73 \begin {gather*} \frac {4}{x}-12\,{\mathrm {e}}^{{\left ({\mathrm {e}}^{{\mathrm {e}}^x}\right )}^{1/12}}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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