Optimal. Leaf size=18 \[ e^{e^{x \left (8+\frac {1}{x^2}+2 x+\log (-2+x)\right )}} \]
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Rubi [F]
time = 17.50, 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 {\exp \left (e^{\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}}+\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}\right ) \left (2-x-16 x^2+x^3+4 x^4+\left (-2 x^2+x^3\right ) \log (-2+x)\right )}{-2 x^2+x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (e^{\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}}+\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}\right ) \left (2-x-16 x^2+x^3+4 x^4+\left (-2 x^2+x^3\right ) \log (-2+x)\right )}{(-2+x) x^2} \, dx\\ &=\int \left (\frac {\exp \left (e^{\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}}+\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}\right ) \left (2-x-16 x^2+x^3+4 x^4\right )}{(-2+x) x^2}+\exp \left (e^{\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}}+\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}\right ) \log (-2+x)\right ) \, dx\\ &=\int \frac {\exp \left (e^{\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}}+\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}\right ) \left (2-x-16 x^2+x^3+4 x^4\right )}{(-2+x) x^2} \, dx+\int \exp \left (e^{\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}}+\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}\right ) \log (-2+x) \, dx\\ &=\int \frac {\exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x} \left (2-x-16 x^2+x^3+4 x^4\right )}{x^2} \, dx+\int \exp \left (e^{\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}}+\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}\right ) \log (-2+x) \, dx\\ &=\int \left (-16 \exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x}+\frac {2 \exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x}}{x^2}-\frac {\exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x}}{x}+\exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x} x+4 \exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x} x^2\right ) \, dx+\int \exp \left (e^{\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}}+\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}\right ) \log (-2+x) \, dx\\ &=2 \int \frac {\exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x}}{x^2} \, dx+4 \int \exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x} x^2 \, dx-16 \int \exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x} \, dx-\int \frac {\exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x}}{x} \, dx+\int \exp \left (e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x+\frac {1}{x}+8 x+2 x^2\right ) (-2+x)^{-1+x} x \, dx+\int \exp \left (e^{\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}}+\frac {1+8 x^2+2 x^3+x^2 \log (-2+x)}{x}\right ) \log (-2+x) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 5.08, size = 22, normalized size = 1.22 \begin {gather*} e^{e^{\frac {1}{x}+8 x+2 x^2} (-2+x)^x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.64, size = 25, normalized size = 1.39
method | result | size |
risch | \({\mathrm e}^{\left (x -2\right )^{x} {\mathrm e}^{\frac {2 x^{3}+8 x^{2}+1}{x}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.38, size = 20, normalized size = 1.11 \begin {gather*} e^{\left (e^{\left (2 \, x^{2} + x \log \left (x - 2\right ) + 8 \, x + \frac {1}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 78 vs.
\(2 (16) = 32\).
time = 0.37, size = 78, normalized size = 4.33 \begin {gather*} e^{\left (\frac {2 \, x^{3} + x^{2} \log \left (x - 2\right ) + 8 \, x^{2} + x e^{\left (\frac {2 \, x^{3} + x^{2} \log \left (x - 2\right ) + 8 \, x^{2} + 1}{x}\right )} + 1}{x} - \frac {2 \, x^{3} + x^{2} \log \left (x - 2\right ) + 8 \, x^{2} + 1}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.84, size = 24, normalized size = 1.33 \begin {gather*} e^{e^{\frac {2 x^{3} + x^{2} \log {\left (x - 2 \right )} + 8 x^{2} + 1}{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 = 4.54, size = 21, normalized size = 1.17 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{8\,x}\,{\mathrm {e}}^{1/x}\,{\mathrm {e}}^{2\,x^2}\,{\left (x-2\right )}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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