Optimal. Leaf size=24 \[ \frac {4}{3} \left (-e^2+\frac {-9+\frac {x}{5}}{e^4}+x\right )^2 \]
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Rubi [B] time = 0.01, antiderivative size = 49, normalized size of antiderivative = 2.04, number of steps used = 2, number of rules used = 1, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {12} \begin {gather*} \frac {4 x^2}{75 e^8}+\frac {2 \left (-2 x+e^2+45\right )^2}{15 e^4}+\frac {4}{3} \left (e^2-x\right )^2-\frac {24 x}{5 e^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-360+8 x+e^4 \left (-1800-40 e^2+80 x\right )+e^8 \left (-200 e^2+200 x\right )\right ) \, dx}{75 e^8}\\ &=\frac {2 \left (45+e^2-2 x\right )^2}{15 e^4}+\frac {4}{3} \left (e^2-x\right )^2-\frac {24 x}{5 e^8}+\frac {4 x^2}{75 e^8}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 41, normalized size = 1.71 \begin {gather*} -\frac {8 \left (1+5 e^4\right ) \left (45 x+5 e^6 x-\frac {x^2}{2}-\frac {5 e^4 x^2}{2}\right )}{75 e^8} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.86, size = 39, normalized size = 1.62 \begin {gather*} \frac {4}{75} \, {\left (25 \, x^{2} e^{8} + x^{2} - 50 \, x e^{10} - 10 \, x e^{6} + 10 \, {\left (x^{2} - 45 \, x\right )} e^{4} - 90 \, x\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 40, normalized size = 1.67 \begin {gather*} \frac {4}{75} \, {\left (x^{2} + 25 \, {\left (x^{2} - 2 \, x e^{2}\right )} e^{8} + 10 \, {\left (x^{2} - x e^{2} - 45 \, x\right )} e^{4} - 90 \, x\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 32, normalized size = 1.33
method | result | size |
gosper | \(-\frac {4 \left (1+5 \,{\mathrm e}^{4}\right ) x \left (10 \,{\mathrm e}^{2} {\mathrm e}^{4}-5 x \,{\mathrm e}^{4}-x +90\right ) {\mathrm e}^{-8}}{75}\) | \(32\) |
risch | \(-\frac {8 \,{\mathrm e}^{2} x}{3}+\frac {4 x^{2}}{3}-\frac {8 x \,{\mathrm e}^{-2}}{15}+\frac {8 x^{2} {\mathrm e}^{-4}}{15}-24 x \,{\mathrm e}^{-4}+\frac {4 x^{2} {\mathrm e}^{-8}}{75}-\frac {24 \,{\mathrm e}^{-8} x}{5}\) | \(41\) |
default | \(\frac {{\mathrm e}^{-8} \left ({\mathrm e}^{8} \left (-200 \,{\mathrm e}^{2} x +100 x^{2}\right )+{\mathrm e}^{4} \left (-40 \,{\mathrm e}^{2} x +40 x^{2}-1800 x \right )+4 x^{2}-360 x \right )}{75}\) | \(53\) |
norman | \(\left (\frac {4 \left (25 \,{\mathrm e}^{8}+10 \,{\mathrm e}^{4}+1\right ) {\mathrm e}^{-4} x^{2}}{75}-\frac {8 \left (5 \,{\mathrm e}^{2} {\mathrm e}^{8}+{\mathrm e}^{2} {\mathrm e}^{4}+45 \,{\mathrm e}^{4}+9\right ) {\mathrm e}^{-4} x}{15}\right ) {\mathrm e}^{-4}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.43, size = 40, normalized size = 1.67 \begin {gather*} \frac {4}{75} \, {\left (x^{2} + 25 \, {\left (x^{2} - 2 \, x e^{2}\right )} e^{8} + 10 \, {\left (x^{2} - x e^{2} - 45 \, x\right )} e^{4} - 90 \, x\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.37, size = 23, normalized size = 0.96 \begin {gather*} \frac {4\,x\,{\mathrm {e}}^{-8}\,\left (5\,{\mathrm {e}}^4+1\right )\,\left (x-10\,{\mathrm {e}}^6+5\,x\,{\mathrm {e}}^4-90\right )}{75} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 44, normalized size = 1.83 \begin {gather*} \frac {x^{2} \left (4 + 40 e^{4} + 100 e^{8}\right )}{75 e^{8}} + \frac {x \left (- 40 e^{10} - 360 e^{4} - 8 e^{6} - 72\right )}{15 e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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