Optimal. Leaf size=22 \[ \frac {1}{4}-\left (3+x+e^{-2 e^4} x^3\right )^4 \]
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Rubi [A] time = 0.04, antiderivative size = 26, normalized size of antiderivative = 1.18, number of steps used = 2, number of rules used = 2, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {12, 1588} \begin {gather*} -e^{-8 e^4} \left (x^3+e^{2 e^4} (x+3)\right )^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1588
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-8 e^4} \int \left (-4 e^{2 e^4}-12 x^2\right ) \left (x^3+e^{2 e^4} (3+x)\right )^3 \, dx\\ &=-e^{-8 e^4} \left (x^3+e^{2 e^4} (3+x)\right )^4\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.05, size = 84, normalized size = 3.82 \begin {gather*} -e^{-8 e^4} \left (x^{12}+4 e^{2 e^4} x^9 (3+x)+6 e^{4 e^4} x^6 (3+x)^2+4 e^{6 e^4} x^3 (3+x)^3+e^{8 e^4} x \left (108+54 x+12 x^2+x^3\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.67, size = 97, normalized size = 4.41 \begin {gather*} -{\left (x^{12} + {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x\right )} e^{\left (8 \, e^{4}\right )} + 4 \, {\left (x^{6} + 9 \, x^{5} + 27 \, x^{4} + 27 \, x^{3}\right )} e^{\left (6 \, e^{4}\right )} + 6 \, {\left (x^{8} + 6 \, x^{7} + 9 \, x^{6}\right )} e^{\left (4 \, e^{4}\right )} + 4 \, {\left (x^{10} + 3 \, x^{9}\right )} e^{\left (2 \, e^{4}\right )}\right )} e^{\left (-8 \, e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.19, size = 79, normalized size = 3.59 \begin {gather*} -{\left ({\left (x^{3} + x e^{\left (2 \, e^{4}\right )}\right )}^{4} + 12 \, {\left (x^{3} + x e^{\left (2 \, e^{4}\right )}\right )}^{3} e^{\left (2 \, e^{4}\right )} + 54 \, {\left (x^{3} + x e^{\left (2 \, e^{4}\right )}\right )}^{2} e^{\left (4 \, e^{4}\right )} + 108 \, {\left (x^{3} + x e^{\left (2 \, e^{4}\right )}\right )} e^{\left (6 \, e^{4}\right )}\right )} e^{\left (-8 \, e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.07, size = 135, normalized size = 6.14
method | result | size |
norman | \(\left (-{\mathrm e}^{-{\mathrm e}^{4}} x^{12}-12 \,{\mathrm e}^{{\mathrm e}^{4}} x^{9}-4 \,{\mathrm e}^{{\mathrm e}^{4}} x^{10}-36 \,{\mathrm e}^{3 \,{\mathrm e}^{4}} x^{7}-6 \,{\mathrm e}^{3 \,{\mathrm e}^{4}} x^{8}-36 \,{\mathrm e}^{5 \,{\mathrm e}^{4}} x^{5}-108 \,{\mathrm e}^{7 \,{\mathrm e}^{4}} x -54 \,{\mathrm e}^{7 \,{\mathrm e}^{4}} x^{2}-2 \,{\mathrm e}^{3 \,{\mathrm e}^{4}} \left (2 \,{\mathrm e}^{2 \,{\mathrm e}^{4}}+27\right ) x^{6}-12 \,{\mathrm e}^{5 \,{\mathrm e}^{4}} \left ({\mathrm e}^{2 \,{\mathrm e}^{4}}+9\right ) x^{3}-{\mathrm e}^{5 \,{\mathrm e}^{4}} \left ({\mathrm e}^{2 \,{\mathrm e}^{4}}+108\right ) x^{4}\right ) {\mathrm e}^{-7 \,{\mathrm e}^{4}}\) | \(135\) |
gosper | \(-x \left (x^{3} {\mathrm e}^{8 \,{\mathrm e}^{4}}+4 \,{\mathrm e}^{6 \,{\mathrm e}^{4}} x^{5}+6 \,{\mathrm e}^{4 \,{\mathrm e}^{4}} x^{7}+4 \,{\mathrm e}^{2 \,{\mathrm e}^{4}} x^{9}+x^{11}+12 \,{\mathrm e}^{8 \,{\mathrm e}^{4}} x^{2}+36 \,{\mathrm e}^{6 \,{\mathrm e}^{4}} x^{4}+36 \,{\mathrm e}^{4 \,{\mathrm e}^{4}} x^{6}+12 \,{\mathrm e}^{2 \,{\mathrm e}^{4}} x^{8}+54 \,{\mathrm e}^{8 \,{\mathrm e}^{4}} x +108 x^{3} {\mathrm e}^{6 \,{\mathrm e}^{4}}+54 x^{5} {\mathrm e}^{4 \,{\mathrm e}^{4}}+108 \,{\mathrm e}^{8 \,{\mathrm e}^{4}}+108 x^{2} {\mathrm e}^{6 \,{\mathrm e}^{4}}\right ) {\mathrm e}^{-8 \,{\mathrm e}^{4}}\) | \(137\) |
default | \({\mathrm e}^{-8 \,{\mathrm e}^{4}} \left (-x^{12}-4 \,{\mathrm e}^{2 \,{\mathrm e}^{4}} x^{10}-12 \,{\mathrm e}^{2 \,{\mathrm e}^{4}} x^{9}-6 \,{\mathrm e}^{4 \,{\mathrm e}^{4}} x^{8}-36 \,{\mathrm e}^{4 \,{\mathrm e}^{4}} x^{7}+\frac {\left (-24 \,{\mathrm e}^{6 \,{\mathrm e}^{4}}-324 \,{\mathrm e}^{4 \,{\mathrm e}^{4}}\right ) x^{6}}{6}-36 \,{\mathrm e}^{6 \,{\mathrm e}^{4}} x^{5}+\frac {\left (-4 \,{\mathrm e}^{2 \,{\mathrm e}^{4}} \left ({\mathrm e}^{6 \,{\mathrm e}^{4}}+27 \,{\mathrm e}^{4 \,{\mathrm e}^{4}}\right )-324 \,{\mathrm e}^{6 \,{\mathrm e}^{4}}\right ) x^{4}}{4}+\frac {\left (-36 \,{\mathrm e}^{8 \,{\mathrm e}^{4}}-324 \,{\mathrm e}^{6 \,{\mathrm e}^{4}}\right ) x^{3}}{3}-54 \,{\mathrm e}^{8 \,{\mathrm e}^{4}} x^{2}-108 \,{\mathrm e}^{8 \,{\mathrm e}^{4}} x \right )\) | \(154\) |
risch | \(-{\mathrm e}^{-8 \,{\mathrm e}^{4}} x^{12}-4 \,{\mathrm e}^{-6 \,{\mathrm e}^{4}} x^{10}-12 \,{\mathrm e}^{-6 \,{\mathrm e}^{4}} x^{9}-6 \,{\mathrm e}^{-4 \,{\mathrm e}^{4}} x^{8}-36 \,{\mathrm e}^{-4 \,{\mathrm e}^{4}} x^{7}-4 \,{\mathrm e}^{-8 \,{\mathrm e}^{4}} x^{6} {\mathrm e}^{6 \,{\mathrm e}^{4}}-54 \,{\mathrm e}^{-8 \,{\mathrm e}^{4}} x^{6} {\mathrm e}^{4 \,{\mathrm e}^{4}}-36 \,{\mathrm e}^{-2 \,{\mathrm e}^{4}} x^{5}-{\mathrm e}^{-8 \,{\mathrm e}^{4}} {\mathrm e}^{6 \,{\mathrm e}^{4}} {\mathrm e}^{2 \,{\mathrm e}^{4}} x^{4}-27 \,{\mathrm e}^{-8 \,{\mathrm e}^{4}} {\mathrm e}^{4 \,{\mathrm e}^{4}} {\mathrm e}^{2 \,{\mathrm e}^{4}} x^{4}-81 \,{\mathrm e}^{-8 \,{\mathrm e}^{4}} {\mathrm e}^{6 \,{\mathrm e}^{4}} x^{4}-12 \,{\mathrm e}^{-8 \,{\mathrm e}^{4}} x^{3} {\mathrm e}^{8 \,{\mathrm e}^{4}}-108 \,{\mathrm e}^{-8 \,{\mathrm e}^{4}} x^{3} {\mathrm e}^{6 \,{\mathrm e}^{4}}-54 x^{2}-108 x\) | \(185\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 22, normalized size = 1.00 \begin {gather*} -{\left (x^{3} + {\left (x + 3\right )} e^{\left (2 \, e^{4}\right )}\right )}^{4} e^{\left (-8 \, e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.09, size = 122, normalized size = 5.55 \begin {gather*} -{\mathrm {e}}^{-8\,{\mathrm {e}}^4}\,x^{12}-4\,{\mathrm {e}}^{-6\,{\mathrm {e}}^4}\,x^{10}-12\,{\mathrm {e}}^{-6\,{\mathrm {e}}^4}\,x^9-6\,{\mathrm {e}}^{-4\,{\mathrm {e}}^4}\,x^8-36\,{\mathrm {e}}^{-4\,{\mathrm {e}}^4}\,x^7-2\,{\mathrm {e}}^{-4\,{\mathrm {e}}^4}\,\left (2\,{\mathrm {e}}^{2\,{\mathrm {e}}^4}+27\right )\,x^6-36\,{\mathrm {e}}^{-2\,{\mathrm {e}}^4}\,x^5-{\mathrm {e}}^{-2\,{\mathrm {e}}^4}\,\left ({\mathrm {e}}^{2\,{\mathrm {e}}^4}+108\right )\,x^4-12\,{\mathrm {e}}^{-2\,{\mathrm {e}}^4}\,\left ({\mathrm {e}}^{2\,{\mathrm {e}}^4}+9\right )\,x^3-54\,x^2-108\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.09, size = 141, normalized size = 6.41 \begin {gather*} - \frac {x^{12}}{e^{8 e^{4}}} - \frac {4 x^{10}}{e^{6 e^{4}}} - \frac {12 x^{9}}{e^{6 e^{4}}} - \frac {6 x^{8}}{e^{4 e^{4}}} - \frac {36 x^{7}}{e^{4 e^{4}}} + \frac {x^{6} \left (- 4 e^{2 e^{4}} - 54\right )}{e^{4 e^{4}}} - \frac {36 x^{5}}{e^{2 e^{4}}} + \frac {x^{4} \left (- e^{2 e^{4}} - 108\right )}{e^{2 e^{4}}} + \frac {x^{3} \left (- 12 e^{2 e^{4}} - 108\right )}{e^{2 e^{4}}} - 54 x^{2} - 108 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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