Optimal. Leaf size=36 \[ \frac {1}{5} e^{-x+\frac {\left (x \left (-1-2 x+\frac {x^2}{2}\right )+2 \log (x)\right )^2}{x}} x \]
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Rubi [F] time = 9.26, 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 (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \left (-12 x-32 x^2+40 x^3+36 x^4-32 x^5+5 x^6+\left (32-32 x^2+16 x^3\right ) \log (x)-16 \log ^2(x)\right )}{20 x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{20} \int \frac {\exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \left (-12 x-32 x^2+40 x^3+36 x^4-32 x^5+5 x^6+\left (32-32 x^2+16 x^3\right ) \log (x)-16 \log ^2(x)\right )}{x} \, dx\\ &=\frac {1}{20} \int \left (-12 \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right )-32 \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x+40 \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^2+36 \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^3-32 \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^4+5 \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^5+\frac {16 \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \left (2-2 x^2+x^3\right ) \log (x)}{x}-\frac {16 \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \log ^2(x)}{x}\right ) \, dx\\ &=\frac {1}{4} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^5 \, dx-\frac {3}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \, dx+\frac {4}{5} \int \frac {\exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \left (2-2 x^2+x^3\right ) \log (x)}{x} \, dx-\frac {4}{5} \int \frac {\exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \log ^2(x)}{x} \, dx-\frac {8}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x \, dx-\frac {8}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^4 \, dx+\frac {9}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^3 \, dx+2 \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^2 \, dx\\ &=\frac {1}{4} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^5 \, dx-\frac {3}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \, dx-\frac {4}{5} \int \frac {\exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \log ^2(x)}{x} \, dx+\frac {4}{5} \int \left (\frac {2 \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \log (x)}{x}-2 \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x \log (x)+\exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^2 \log (x)\right ) \, dx-\frac {8}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x \, dx-\frac {8}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^4 \, dx+\frac {9}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^3 \, dx+2 \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^2 \, dx\\ &=\frac {1}{4} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^5 \, dx-\frac {3}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \, dx+\frac {4}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^2 \log (x) \, dx-\frac {4}{5} \int \frac {\exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \log ^2(x)}{x} \, dx-\frac {8}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x \, dx-\frac {8}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^4 \, dx+\frac {8}{5} \int \frac {\exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) \log (x)}{x} \, dx-\frac {8}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x \log (x) \, dx+\frac {9}{5} \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^3 \, dx+2 \int \exp \left (-\frac {-16 x^3-12 x^4+8 x^5-x^6+\left (16 x+32 x^2-8 x^3\right ) \log (x)-16 \log ^2(x)}{4 x}\right ) x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 48, normalized size = 1.33 \begin {gather*} \frac {1}{5} e^{4 x^2+3 x^3-2 x^4+\frac {x^5}{4}+\frac {4 \log ^2(x)}{x}} x^{-3+2 (-4+x) x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 50, normalized size = 1.39 \begin {gather*} \frac {1}{5} \, x e^{\left (\frac {x^{6} - 8 \, x^{5} + 12 \, x^{4} + 16 \, x^{3} + 8 \, {\left (x^{3} - 4 \, x^{2} - 2 \, x\right )} \log \relax (x) + 16 \, \log \relax (x)^{2}}{4 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.59, size = 53, normalized size = 1.47 \begin {gather*} \frac {1}{5} \, x e^{\left (\frac {x^{6} - 8 \, x^{5} + 12 \, x^{4} + 8 \, x^{3} \log \relax (x) + 16 \, x^{3} - 32 \, x^{2} \log \relax (x) - 16 \, x \log \relax (x) + 16 \, \log \relax (x)^{2}}{4 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 39, normalized size = 1.08
method | result | size |
risch | \(\frac {x \,{\mathrm e}^{\frac {\left (x^{3}-4 x^{2}+4 \ln \relax (x )\right ) \left (x^{3}-4 x^{2}+4 \ln \relax (x )-4 x \right )}{4 x}}}{5}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.83, size = 48, normalized size = 1.33 \begin {gather*} \frac {e^{\left (\frac {1}{4} \, x^{5} - 2 \, x^{4} + 3 \, x^{3} + 2 \, x^{2} \log \relax (x) + 4 \, x^{2} - 8 \, x \log \relax (x) + \frac {4 \, \log \relax (x)^{2}}{x}\right )}}{5 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.92, size = 48, normalized size = 1.33 \begin {gather*} \frac {x^{2\,x^2-8\,x-3}\,{\mathrm {e}}^{4\,x^2}\,{\mathrm {e}}^{3\,x^3}\,{\mathrm {e}}^{-2\,x^4}\,{\mathrm {e}}^{\frac {x^5}{4}}\,{\mathrm {e}}^{\frac {4\,{\ln \relax (x)}^2}{x}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.50, size = 51, normalized size = 1.42 \begin {gather*} \frac {x e^{- \frac {- \frac {x^{6}}{4} + 2 x^{5} - 3 x^{4} - 4 x^{3} + \frac {\left (- 8 x^{3} + 32 x^{2} + 16 x\right ) \log {\relax (x )}}{4} - 4 \log {\relax (x )}^{2}}{x}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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