Optimal. Leaf size=31 \[ \frac {x^2}{11}+\frac {x-3 \left (e^{\frac {5+e^{e^5}}{x}}+x\right )}{x} \]
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Rubi [A]
time = 0.07, antiderivative size = 26, normalized size of antiderivative = 0.84, number of steps
used = 4, number of rules used = 3, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 14, 2326}
\begin {gather*} \frac {x^2}{11}-\frac {3 e^{\frac {5+e^{e^5}}{x}}}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{11} \int \frac {2 x^4+e^{\frac {5+e^{e^5}}{x}} \left (165+33 e^{e^5}+33 x\right )}{x^3} \, dx\\ &=\frac {1}{11} \int \left (2 x+\frac {33 e^{\frac {5+e^{e^5}}{x}} \left (5+e^{e^5}+x\right )}{x^3}\right ) \, dx\\ &=\frac {x^2}{11}+3 \int \frac {e^{\frac {5+e^{e^5}}{x}} \left (5+e^{e^5}+x\right )}{x^3} \, dx\\ &=-\frac {3 e^{\frac {5+e^{e^5}}{x}}}{x}+\frac {x^2}{11}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 26, normalized size = 0.84 \begin {gather*} -\frac {3 e^{\frac {5+e^{e^5}}{x}}}{x}+\frac {x^2}{11} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(160\) vs.
\(2(26)=52\).
time = 0.31, size = 161, normalized size = 5.19
method | result | size |
risch | \(\frac {x^{2}}{11}-\frac {3 \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}\) | \(22\) |
norman | \(\frac {\frac {x^{4}}{11}-3 \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}} x}{x^{2}}\) | \(24\) |
derivativedivides | \(-\frac {-\frac {625 x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {500 \,{\mathrm e}^{{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {150 \,{\mathrm e}^{2 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {20 \,{\mathrm e}^{3 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {{\mathrm e}^{4 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}+\frac {165 \left ({\mathrm e}^{{\mathrm e}^{5}}+5\right ) {\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}+33 \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}} {\mathrm e}^{{\mathrm e}^{5}}+33 \,{\mathrm e}^{{\mathrm e}^{5}} \left (\frac {\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right ) {\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}-{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}\right )}{11 \left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}\) | \(161\) |
default | \(-\frac {-\frac {625 x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {500 \,{\mathrm e}^{{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {150 \,{\mathrm e}^{2 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {20 \,{\mathrm e}^{3 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}-\frac {{\mathrm e}^{4 \,{\mathrm e}^{5}} x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}+\frac {165 \left ({\mathrm e}^{{\mathrm e}^{5}}+5\right ) {\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}+33 \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}} {\mathrm e}^{{\mathrm e}^{5}}+33 \,{\mathrm e}^{{\mathrm e}^{5}} \left (\frac {\left ({\mathrm e}^{{\mathrm e}^{5}}+5\right ) {\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}}{x}-{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{5}}+5}{x}}\right )}{11 \left ({\mathrm e}^{{\mathrm e}^{5}}+5\right )^{2}}\) | \(161\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 21, normalized size = 0.68 \begin {gather*} \frac {x^{3} - 33 \, e^{\left (\frac {e^{\left (e^{5}\right )} + 5}{x}\right )}}{11 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 17, normalized size = 0.55 \begin {gather*} \frac {x^{2}}{11} - \frac {3 e^{\frac {5 + e^{e^{5}}}{x}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 55 vs.
\(2 (27) = 54\).
time = 0.40, size = 55, normalized size = 1.77 \begin {gather*} -\frac {x^{2} {\left (\frac {33 \, {\left (e^{\left (e^{5}\right )} + 5\right )}^{3} e^{\left (\frac {e^{\left (e^{5}\right )} + 5}{x}\right )}}{x^{3}} - e^{\left (3 \, e^{5}\right )} - 15 \, e^{\left (2 \, e^{5}\right )} - 75 \, e^{\left (e^{5}\right )} - 125\right )}}{11 \, {\left (e^{\left (e^{5}\right )} + 5\right )}^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.17, size = 25, normalized size = 0.81 \begin {gather*} \frac {x^2}{11}-\frac {3\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^5}}{x}}\,{\mathrm {e}}^{5/x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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