Optimal. Leaf size=30 \[ 4+x+\frac {\frac {1}{5} e^{e^{\frac {5 \left (-5+x-x^2\right )}{x}}}+x}{x} \]
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Rubi [F]
time = 0.85, 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 {5 x^3+e^{e^{\frac {-25+5 x-5 x^2}{x}}} \left (-x+e^{\frac {-25+5 x-5 x^2}{x}} \left (25-5 x^2\right )\right )}{5 x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {5 x^3+e^{e^{\frac {-25+5 x-5 x^2}{x}}} \left (-x+e^{\frac {-25+5 x-5 x^2}{x}} \left (25-5 x^2\right )\right )}{x^3} \, dx\\ &=\frac {1}{5} \int \left (-\frac {5 e^{5+e^{5-\frac {25}{x}-5 x}-\frac {25}{x}-5 x} \left (-5+x^2\right )}{x^3}+\frac {-e^{e^{5-\frac {25}{x}-5 x}}+5 x^2}{x^2}\right ) \, dx\\ &=\frac {1}{5} \int \frac {-e^{e^{5-\frac {25}{x}-5 x}}+5 x^2}{x^2} \, dx-\int \frac {e^{5+e^{5-\frac {25}{x}-5 x}-\frac {25}{x}-5 x} \left (-5+x^2\right )}{x^3} \, dx\\ &=\frac {1}{5} \int \left (5-\frac {e^{e^{5-\frac {25}{x}-5 x}}}{x^2}\right ) \, dx-\int \left (-\frac {5 e^{5+e^{5-\frac {25}{x}-5 x}-\frac {25}{x}-5 x}}{x^3}+\frac {e^{5+e^{5-\frac {25}{x}-5 x}-\frac {25}{x}-5 x}}{x}\right ) \, dx\\ &=x-\frac {1}{5} \int \frac {e^{e^{5-\frac {25}{x}-5 x}}}{x^2} \, dx+5 \int \frac {e^{5+e^{5-\frac {25}{x}-5 x}-\frac {25}{x}-5 x}}{x^3} \, dx-\int \frac {e^{5+e^{5-\frac {25}{x}-5 x}-\frac {25}{x}-5 x}}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.35, size = 23, normalized size = 0.77 \begin {gather*} \frac {e^{e^{5-\frac {25}{x}-5 x}}}{5 x}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.10, size = 23, normalized size = 0.77
method | result | size |
risch | \(x +\frac {{\mathrm e}^{{\mathrm e}^{-\frac {5 \left (x^{2}-x +5\right )}{x}}}}{5 x}\) | \(23\) |
norman | \(\frac {x^{3}+\frac {x \,{\mathrm e}^{{\mathrm e}^{\frac {-5 x^{2}+5 x -25}{x}}}}{5}}{x^{2}}\) | \(28\) |
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 = 0.35, size = 26, normalized size = 0.87 \begin {gather*} \frac {5 \, x^{2} + e^{\left (e^{\left (-\frac {5 \, {\left (x^{2} - x + 5\right )}}{x}\right )}\right )}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 19, normalized size = 0.63 \begin {gather*} x + \frac {e^{e^{\frac {- 5 x^{2} + 5 x - 25}{x}}}}{5 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 = 3.51, size = 21, normalized size = 0.70 \begin {gather*} x+\frac {{\mathrm {e}}^{{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^5\,{\mathrm {e}}^{-\frac {25}{x}}}}{5\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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