Optimal. Leaf size=31 \[ \frac {5}{-2 x+\left (-4+e^5+e x\right )^2+\frac {4-\frac {x^3}{3}}{x}} \]
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Rubi [F]
time = 180.07, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [A]
time = 0.04, size = 41, normalized size = 1.32 \begin {gather*} \frac {15 x}{12+3 \left (-4+e^5\right )^2 x+6 \left (-1-4 e+e^6\right ) x^2+\left (-1+3 e^2\right ) x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 1.50, size = 409, normalized size = 13.19
method | result | size |
risch | \(\frac {5 x}{x \,{\mathrm e}^{10}+2 x^{2} {\mathrm e}^{6}-8 x \,{\mathrm e}^{5}+x^{3} {\mathrm e}^{2}-8 x^{2} {\mathrm e}-\frac {x^{3}}{3}-2 x^{2}+16 x +4}\) | \(50\) |
gosper | \(\frac {15 x}{3 x^{3} {\mathrm e}^{2}+6 x^{2} {\mathrm e} \,{\mathrm e}^{5}+3 x \,{\mathrm e}^{10}-24 x^{2} {\mathrm e}-x^{3}-24 x \,{\mathrm e}^{5}-6 x^{2}+48 x +12}\) | \(58\) |
norman | \(\frac {15 x}{3 x^{3} {\mathrm e}^{2}+6 x^{2} {\mathrm e} \,{\mathrm e}^{5}+3 x \,{\mathrm e}^{10}-24 x^{2} {\mathrm e}-x^{3}-24 x \,{\mathrm e}^{5}-6 x^{2}+48 x +12}\) | \(58\) |
default | \(5 \left (\munderset {\textit {\_R} =\RootOf \left (-144-\left (-6 \,{\mathrm e}^{2}+9 \,{\mathrm e}^{4}+1\right ) \textit {\_Z}^{6}-\left (-36 \,{\mathrm e}^{2}+48 \,{\mathrm e}-144 \,{\mathrm e}^{3}-12 \,{\mathrm e}^{6}+36 \,{\mathrm e}^{8}+12\right ) \textit {\_Z}^{5}-\left (48 \,{\mathrm e}^{5}+864 \,{\mathrm e}^{2}+288 \,{\mathrm e}-6 \,{\mathrm e}^{10}-72 \,{\mathrm e}^{6}-432 \,{\mathrm e}^{7}+54 \,{\mathrm e}^{12}-60\right ) \textit {\_Z}^{4}-\left (288 \,{\mathrm e}^{5}+72 \,{\mathrm e}^{2}-2304 \,{\mathrm e}+36 \,{\mathrm e}^{16}-36 \,{\mathrm e}^{10}+1728 \,{\mathrm e}^{6}-432 \,{\mathrm e}^{11}-600\right ) \textit {\_Z}^{3}-\left (-2304 \,{\mathrm e}^{5}-576 \,{\mathrm e}+9 \,{\mathrm e}^{20}+864 \,{\mathrm e}^{10}+144 \,{\mathrm e}^{6}-144 \,{\mathrm e}^{15}+2160\right ) \textit {\_Z}^{2}-\left (-576 \,{\mathrm e}^{5}+72 \,{\mathrm e}^{10}+1152\right ) \textit {\_Z} \right )}{\sum }\frac {\left (6+\left (-3 \,{\mathrm e}^{2}+1\right ) \textit {\_R}^{3}+3 \left (1+4 \,{\mathrm e}-{\mathrm e}^{6}\right ) \textit {\_R}^{2}\right ) \ln \left (x -\textit {\_R} \right )}{192+720 \textit {\_R} +576 \textit {\_R}^{3} {\mathrm e}^{2}+40 \textit {\_R}^{4} {\mathrm e}-1152 \textit {\_R}^{2} {\mathrm e}-192 \textit {\_R} \,{\mathrm e}+12 \,{\mathrm e}^{10}-96 \,{\mathrm e}^{5}+\textit {\_R}^{5}+10 \textit {\_R}^{4}-300 \textit {\_R}^{2}-40 \textit {\_R}^{3}-48 \textit {\_R} \,{\mathrm e}^{15}+192 \textit {\_R}^{3} {\mathrm e}-48 \textit {\_R}^{3} {\mathrm e}^{6}-120 \textit {\_R}^{4} {\mathrm e}^{3}+864 \textit {\_R}^{2} {\mathrm e}^{6}+48 \textit {\_R} \,{\mathrm e}^{6}-10 \textit {\_R}^{4} {\mathrm e}^{6}+18 \textit {\_R}^{2} {\mathrm e}^{16}+3 \textit {\_R} \,{\mathrm e}^{20}+36 \,{\mathrm e}^{12} \textit {\_R}^{3}+32 \textit {\_R}^{3} {\mathrm e}^{5}-4 \textit {\_R}^{3} {\mathrm e}^{10}-216 \textit {\_R}^{2} {\mathrm e}^{11}-288 \textit {\_R}^{3} {\mathrm e}^{7}+288 \textit {\_R} \,{\mathrm e}^{10}-768 \textit {\_R} \,{\mathrm e}^{5}-18 \,{\mathrm e}^{10} \textit {\_R}^{2}+144 \textit {\_R}^{2} {\mathrm e}^{5}-6 \,{\mathrm e}^{2} \textit {\_R}^{5}+36 \textit {\_R}^{2} {\mathrm e}^{2}-30 \textit {\_R}^{4} {\mathrm e}^{2}+9 \textit {\_R}^{5} {\mathrm e}^{4}+30 \textit {\_R}^{4} {\mathrm e}^{8}}\right )\) | \(409\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.38, size = 41, normalized size = 1.32 \begin {gather*} \frac {15 \, x}{x^{3} {\left (3 \, e^{2} - 1\right )} + 6 \, x^{2} {\left (e^{6} - 4 \, e - 1\right )} + 3 \, x {\left (e^{10} - 8 \, e^{5} + 16\right )} + 12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 51, normalized size = 1.65 \begin {gather*} \frac {15 \, x}{3 \, x^{3} e^{2} - x^{3} + 6 \, x^{2} e^{6} - 24 \, x^{2} e - 6 \, x^{2} + 3 \, x e^{10} - 24 \, x e^{5} + 48 \, x + 12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 9.94, size = 42, normalized size = 1.35 \begin {gather*} \frac {15 x}{x^{3} \left (-1 + 3 e^{2}\right ) + x^{2} \left (- 24 e - 6 + 6 e^{6}\right ) + x \left (- 24 e^{5} + 48 + 3 e^{10}\right ) + 12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 51, normalized size = 1.65 \begin {gather*} \frac {15 \, x}{3 \, x^{3} e^{2} - x^{3} + 6 \, x^{2} e^{6} - 24 \, x^{2} e - 6 \, x^{2} + 3 \, x e^{10} - 24 \, x e^{5} + 48 \, x + 12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.48, size = 44, normalized size = 1.42 \begin {gather*} \frac {15\,x}{\left (3\,{\mathrm {e}}^2-1\right )\,x^3+\left (6\,{\mathrm {e}}^6-24\,\mathrm {e}-6\right )\,x^2+\left (3\,{\mathrm {e}}^{10}-24\,{\mathrm {e}}^5+48\right )\,x+12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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