Optimal. Leaf size=22 \[ -4+e^{\left (2+e^{-6+x} x\right )^2} (4-\log (x)) \]
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Rubi [B] time = 0.68, antiderivative size = 126, normalized size of antiderivative = 5.73, number of steps used = 1, number of rules used = 1, integrand size = 101, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {2288} \begin {gather*} \frac {e^{e^{2 x-12} x^2+4 e^{x-6} x+4} \left (8 e^{x-6} \left (x^2+x\right )+4 e^{2 x-12} \left (x^3+x^2\right )-\left (2 e^{x-6} \left (x^2+x\right )+e^{2 x-12} \left (x^3+x^2\right )\right ) \log (x)\right )}{x \left (e^{2 x-12} x^2+2 e^{x-6} x+e^{2 x-12} x+2 e^{x-6}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{4+4 e^{-6+x} x+e^{-12+2 x} x^2} \left (8 e^{-6+x} \left (x+x^2\right )+4 e^{-12+2 x} \left (x^2+x^3\right )-\left (2 e^{-6+x} \left (x+x^2\right )+e^{-12+2 x} \left (x^2+x^3\right )\right ) \log (x)\right )}{x \left (2 e^{-6+x}+2 e^{-6+x} x+e^{-12+2 x} x+e^{-12+2 x} x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.57, size = 25, normalized size = 1.14 \begin {gather*} -e^{\frac {\left (2 e^6+e^x x\right )^2}{e^{12}}} (-4+\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 26, normalized size = 1.18 \begin {gather*} -{\left (\log \relax (x) - 4\right )} e^{\left (x^{2} e^{\left (2 \, x - 12\right )} + 4 \, x e^{\left (x - 6\right )} + 4\right )} \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*} \int \frac {{\left (8 \, {\left (x^{3} + x^{2}\right )} e^{\left (2 \, x - 12\right )} + 16 \, {\left (x^{2} + x\right )} e^{\left (x - 6\right )} - 2 \, {\left ({\left (x^{3} + x^{2}\right )} e^{\left (2 \, x - 12\right )} + 2 \, {\left (x^{2} + x\right )} e^{\left (x - 6\right )}\right )} \log \relax (x) - 1\right )} e^{\left (x^{2} e^{\left (2 \, x - 12\right )} + 4 \, x e^{\left (x - 6\right )} + 4\right )}}{x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 28, normalized size = 1.27
method | result | size |
risch | \(\left (-\ln \relax (x )+4\right ) {\mathrm e}^{x^{2} {\mathrm e}^{2 x -12}+4 x \,{\mathrm e}^{x -6}+4}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 31, normalized size = 1.41 \begin {gather*} -{\left (e^{4} \log \relax (x) - 4 \, e^{4}\right )} e^{\left (x^{2} e^{\left (2 \, x - 12\right )} + 4 \, x e^{\left (x - 6\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x-6}+x^2\,{\mathrm {e}}^{2\,x-12}+4}\,\left ({\mathrm {e}}^{x-6}\,\left (16\,x^2+16\,x\right )-\ln \relax (x)\,\left ({\mathrm {e}}^{x-6}\,\left (4\,x^2+4\,x\right )+{\mathrm {e}}^{2\,x-12}\,\left (2\,x^3+2\,x^2\right )\right )+{\mathrm {e}}^{2\,x-12}\,\left (8\,x^3+8\,x^2\right )-1\right )}{x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.65, size = 26, normalized size = 1.18 \begin {gather*} \left (4 - \log {\relax (x )}\right ) e^{x^{2} e^{2 x - 12} + 4 x e^{x - 6} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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