Optimal. Leaf size=26 \[ 2-x \left (x+x^2+\frac {1}{4} e^4 (2+x) (x+2 \log (5))\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 45, normalized size of antiderivative = 1.73, number of steps used = 3, number of rules used = 1, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {12} \begin {gather*} -\frac {1}{4} e^4 x^3-x^3-\frac {e^4 x^2}{2}-x^2-\frac {1}{2} e^4 (x+1)^2 \log (5) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \left (-8 x-12 x^2+e^4 \left (-4 x-3 x^2\right )+e^4 (-4-4 x) \log (5)\right ) \, dx\\ &=-x^2-x^3-\frac {1}{2} e^4 (1+x)^2 \log (5)+\frac {1}{4} e^4 \int \left (-4 x-3 x^2\right ) \, dx\\ &=-x^2-\frac {e^4 x^2}{2}-x^3-\frac {e^4 x^3}{4}-\frac {1}{2} e^4 (1+x)^2 \log (5)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 38, normalized size = 1.46 \begin {gather*} -\frac {1}{4} \left (4+e^4\right ) x^3-e^4 x \log (5)-\frac {1}{2} x^2 \left (2+e^4 (1+\log (5))\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 37, normalized size = 1.42 \begin {gather*} -x^{3} - \frac {1}{2} \, {\left (x^{2} + 2 \, x\right )} e^{4} \log \relax (5) - x^{2} - \frac {1}{4} \, {\left (x^{3} + 2 \, x^{2}\right )} e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.76, size = 37, normalized size = 1.42 \begin {gather*} -x^{3} - \frac {1}{2} \, {\left (x^{2} + 2 \, x\right )} e^{4} \log \relax (5) - x^{2} - \frac {1}{4} \, {\left (x^{3} + 2 \, x^{2}\right )} e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 35, normalized size = 1.35
method | result | size |
norman | \(\left (-\frac {{\mathrm e}^{4}}{4}-1\right ) x^{3}+\left (-\frac {{\mathrm e}^{4} \ln \relax (5)}{2}-\frac {{\mathrm e}^{4}}{2}-1\right ) x^{2}-{\mathrm e}^{4} \ln \relax (5) x\) | \(35\) |
gosper | \(-\frac {x \left (2 \,{\mathrm e}^{4} \ln \relax (5) x +x^{2} {\mathrm e}^{4}+4 \,{\mathrm e}^{4} \ln \relax (5)+2 x \,{\mathrm e}^{4}+4 x^{2}+4 x \right )}{4}\) | \(37\) |
default | \(\frac {{\mathrm e}^{4} \ln \relax (5) \left (-2 x^{2}-4 x \right )}{4}+\frac {{\mathrm e}^{4} \left (-x^{3}-2 x^{2}\right )}{4}-x^{3}-x^{2}\) | \(42\) |
risch | \(-\frac {{\mathrm e}^{4} \ln \relax (5) x^{2}}{2}-{\mathrm e}^{4} \ln \relax (5) x -\frac {x^{3} {\mathrm e}^{4}}{4}-\frac {x^{2} {\mathrm e}^{4}}{2}-x^{3}-x^{2}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 37, normalized size = 1.42 \begin {gather*} -x^{3} - \frac {1}{2} \, {\left (x^{2} + 2 \, x\right )} e^{4} \log \relax (5) - x^{2} - \frac {1}{4} \, {\left (x^{3} + 2 \, x^{2}\right )} e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 36, normalized size = 1.38 \begin {gather*} \left (-\frac {{\mathrm {e}}^4}{4}-1\right )\,x^3+\left (-\frac {{\mathrm {e}}^4}{2}-\frac {{\mathrm {e}}^4\,\ln \relax (5)}{2}-1\right )\,x^2-{\mathrm {e}}^4\,\ln \relax (5)\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 39, normalized size = 1.50 \begin {gather*} x^{3} \left (- \frac {e^{4}}{4} - 1\right ) + x^{2} \left (- \frac {e^{4} \log {\relax (5 )}}{2} - \frac {e^{4}}{2} - 1\right ) - x e^{4} \log {\relax (5 )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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