Optimal. Leaf size=29 \[ -x+\left (e^{\frac {10 \left (3-4 x^2\right )}{x}+x (x+\log (x))}+x\right )^2 \]
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Rubi [F]
time = 1.63, 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 {-x^2+2 x^3+e^{\frac {2 \left (30-40 x^2+x^3+x^2 \log (x)\right )}{x}} \left (-60-78 x^2+4 x^3+2 x^2 \log (x)\right )+e^{\frac {30-40 x^2+x^3+x^2 \log (x)}{x}} \left (-60 x+2 x^2-78 x^3+4 x^4+2 x^3 \log (x)\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+2 x+2 e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{-2+2 x} \left (-30-39 x^2+2 x^3+x^2 \log (x)\right )+2 e^{\frac {30}{x}-40 x+x^2} x^{-1+x} \left (-30+x-39 x^2+2 x^3+x^2 \log (x)\right )\right ) \, dx\\ &=-x+x^2+2 \int e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{-2+2 x} \left (-30-39 x^2+2 x^3+x^2 \log (x)\right ) \, dx+2 \int e^{\frac {30}{x}-40 x+x^2} x^{-1+x} \left (-30+x-39 x^2+2 x^3+x^2 \log (x)\right ) \, dx\\ &=-x+x^2+2 \int \left (-39 e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{2 x}-30 e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{-2+2 x}+2 e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{1+2 x}+e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{2 x} \log (x)\right ) \, dx+2 \int \left (-30 e^{\frac {30}{x}-40 x+x^2} x^{-1+x}+e^{\frac {30}{x}-40 x+x^2} x^x-39 e^{\frac {30}{x}-40 x+x^2} x^{1+x}+2 e^{\frac {30}{x}-40 x+x^2} x^{2+x}+e^{\frac {30}{x}-40 x+x^2} x^{1+x} \log (x)\right ) \, dx\\ &=-x+x^2+2 \int e^{\frac {30}{x}-40 x+x^2} x^x \, dx+2 \int e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{2 x} \log (x) \, dx+2 \int e^{\frac {30}{x}-40 x+x^2} x^{1+x} \log (x) \, dx+4 \int e^{\frac {30}{x}-40 x+x^2} x^{2+x} \, dx+4 \int e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{1+2 x} \, dx-60 \int e^{\frac {30}{x}-40 x+x^2} x^{-1+x} \, dx-60 \int e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{-2+2 x} \, dx-78 \int e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{2 x} \, dx-78 \int e^{\frac {30}{x}-40 x+x^2} x^{1+x} \, dx\\ &=-x+x^2+2 \int e^{\frac {30}{x}-40 x+x^2} x^x \, dx-2 \int \frac {\int e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{2 x} \, dx}{x} \, dx-2 \int \frac {\int e^{\frac {30}{x}-40 x+x^2} x^{1+x} \, dx}{x} \, dx+4 \int e^{\frac {30}{x}-40 x+x^2} x^{2+x} \, dx+4 \int e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{1+2 x} \, dx-60 \int e^{\frac {30}{x}-40 x+x^2} x^{-1+x} \, dx-60 \int e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{-2+2 x} \, dx-78 \int e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{2 x} \, dx-78 \int e^{\frac {30}{x}-40 x+x^2} x^{1+x} \, dx+(2 \log (x)) \int e^{\frac {2 \left (30-40 x^2+x^3\right )}{x}} x^{2 x} \, dx+(2 \log (x)) \int e^{\frac {30}{x}-40 x+x^2} x^{1+x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.73, size = 50, normalized size = 1.72 \begin {gather*} -x+x^2+e^{\frac {60}{x}-80 x+2 x^2} x^{2 x}+2 e^{\frac {30}{x}-40 x+x^2} x^{1+x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.47, size = 54, normalized size = 1.86
method | result | size |
risch | \(x^{2}+2 x^{x} {\mathrm e}^{\frac {x^{3}-40 x^{2}+30}{x}} x +x^{2 x} {\mathrm e}^{\frac {2 x^{3}-80 x^{2}+60}{x}}-x\) | \(51\) |
default | \(-x +2 x \,{\mathrm e}^{\frac {x^{2} \ln \left (x \right )+x^{3}-40 x^{2}+30}{x}}+{\mathrm e}^{\frac {2 x^{2} \ln \left (x \right )+2 x^{3}-80 x^{2}+60}{x}}+x^{2}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 50, normalized size = 1.72 \begin {gather*} x^{2} + {\left (2 \, x e^{\left (x^{2} + x \log \left (x\right ) + 40 \, x + \frac {30}{x}\right )} + e^{\left (2 \, x^{2} + 2 \, x \log \left (x\right ) + \frac {60}{x}\right )}\right )} e^{\left (-80 \, x\right )} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 53, normalized size = 1.83 \begin {gather*} x^{2} + 2 \, x e^{\left (\frac {x^{3} + x^{2} \log \left (x\right ) - 40 \, x^{2} + 30}{x}\right )} - x + e^{\left (\frac {2 \, {\left (x^{3} + x^{2} \log \left (x\right ) - 40 \, x^{2} + 30\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs.
\(2 (20) = 40\).
time = 0.16, size = 51, normalized size = 1.76 \begin {gather*} x^{2} + 2 x e^{\frac {x^{3} + x^{2} \log {\left (x \right )} - 40 x^{2} + 30}{x}} - x + e^{\frac {2 \left (x^{3} + x^{2} \log {\left (x \right )} - 40 x^{2} + 30\right )}{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 = 9.27, size = 47, normalized size = 1.62 \begin {gather*} x^{2\,x}\,{\mathrm {e}}^{\frac {60}{x}-80\,x+2\,x^2}-x+x^2+2\,x\,x^x\,{\mathrm {e}}^{\frac {30}{x}-40\,x+x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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