Optimal. Leaf size=29 \[ \frac {1}{16} \left (1+e^{\frac {\frac {2}{x^2}+x}{x}}\right )^2+\frac {5}{6 x} \]
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Rubi [A] time = 0.06, antiderivative size = 34, normalized size of antiderivative = 1.17, number of steps used = 5, number of rules used = 3, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.075, Rules used = {12, 14, 2209} \begin {gather*} \frac {1}{8} e^{\frac {2}{x^3}+1}+\frac {1}{16} e^{\frac {4}{x^3}+2}+\frac {5}{6 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{12} \int \frac {-9 e^{\frac {2+x^3}{x^3}}-9 e^{\frac {2 \left (2+x^3\right )}{x^3}}-10 x^2}{x^4} \, dx\\ &=\frac {1}{12} \int \left (-\frac {9 e^{1+\frac {2}{x^3}}}{x^4}-\frac {9 e^{2+\frac {4}{x^3}}}{x^4}-\frac {10}{x^2}\right ) \, dx\\ &=\frac {5}{6 x}-\frac {3}{4} \int \frac {e^{1+\frac {2}{x^3}}}{x^4} \, dx-\frac {3}{4} \int \frac {e^{2+\frac {4}{x^3}}}{x^4} \, dx\\ &=\frac {1}{8} e^{1+\frac {2}{x^3}}+\frac {1}{16} e^{2+\frac {4}{x^3}}+\frac {5}{6 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 36, normalized size = 1.24 \begin {gather*} \frac {1}{12} \left (\frac {3}{2} e^{1+\frac {2}{x^3}}+\frac {3}{4} e^{2+\frac {4}{x^3}}+\frac {10}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 34, normalized size = 1.17 \begin {gather*} \frac {3 \, x e^{\left (\frac {2 \, {\left (x^{3} + 2\right )}}{x^{3}}\right )} + 6 \, x e^{\left (\frac {x^{3} + 2}{x^{3}}\right )} + 40}{48 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 26, normalized size = 0.90 \begin {gather*} \frac {5}{6 \, x} + \frac {1}{16} \, e^{\left (\frac {4}{x^{3}} + 2\right )} + \frac {1}{8} \, e^{\left (\frac {2}{x^{3}} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 29, normalized size = 1.00
method | result | size |
derivativedivides | \(\frac {5}{6 x}+\frac {{\mathrm e}^{\frac {2}{x^{3}}} {\mathrm e}}{8}+\frac {{\mathrm e}^{\frac {4}{x^{3}}} {\mathrm e}^{2}}{16}\) | \(29\) |
default | \(\frac {5}{6 x}+\frac {{\mathrm e}^{\frac {2}{x^{3}}} {\mathrm e}}{8}+\frac {{\mathrm e}^{\frac {4}{x^{3}}} {\mathrm e}^{2}}{16}\) | \(29\) |
risch | \(\frac {5}{6 x}+\frac {{\mathrm e}^{\frac {2 x^{3}+4}{x^{3}}}}{16}+\frac {{\mathrm e}^{\frac {x^{3}+2}{x^{3}}}}{8}\) | \(32\) |
norman | \(\frac {\frac {5 x^{2}}{6}+\frac {{\mathrm e}^{\frac {x^{3}+2}{x^{3}}} x^{3}}{8}+\frac {{\mathrm e}^{\frac {2 x^{3}+4}{x^{3}}} x^{3}}{16}}{x^{3}}\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 26, normalized size = 0.90 \begin {gather*} \frac {5}{6 \, x} + \frac {1}{16} \, e^{\left (\frac {4}{x^{3}} + 2\right )} + \frac {1}{8} \, e^{\left (\frac {2}{x^{3}} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.68, size = 26, normalized size = 0.90 \begin {gather*} \frac {\mathrm {e}\,{\mathrm {e}}^{\frac {2}{x^3}}}{8}+\frac {{\mathrm {e}}^2\,{\mathrm {e}}^{\frac {4}{x^3}}}{16}+\frac {5}{6\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 29, normalized size = 1.00 \begin {gather*} \frac {e^{\frac {2 \left (x^{3} + 2\right )}{x^{3}}}}{16} + \frac {e^{\frac {x^{3} + 2}{x^{3}}}}{8} + \frac {5}{6 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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