Optimal. Leaf size=19 \[ \frac {(1-x) x^3 (3+x)^4}{e^{64/3}} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(61\) vs. \(2(19)=38\).
time = 0.01, antiderivative size = 61, normalized size of antiderivative = 3.21, number of steps
used = 2, number of rules used = 1, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {12}
\begin {gather*} -\frac {x^8}{e^{64/3}}-\frac {11 x^7}{e^{64/3}}-\frac {42 x^6}{e^{64/3}}-\frac {54 x^5}{e^{64/3}}+\frac {27 x^4}{e^{64/3}}+\frac {81 x^3}{e^{64/3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (243 x^2+108 x^3-270 x^4-252 x^5-77 x^6-8 x^7\right ) \, dx}{e^{64/3}}\\ &=\frac {81 x^3}{e^{64/3}}+\frac {27 x^4}{e^{64/3}}-\frac {54 x^5}{e^{64/3}}-\frac {42 x^6}{e^{64/3}}-\frac {11 x^7}{e^{64/3}}-\frac {x^8}{e^{64/3}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 36, normalized size = 1.89 \begin {gather*} -\frac {-81 x^3-27 x^4+54 x^5+42 x^6+11 x^7+x^8}{e^{64/3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.39, size = 41, normalized size = 2.16
method | result | size |
gosper | \(-\left (x^{5}+11 x^{4}+42 x^{3}+54 x^{2}-27 x -81\right ) x^{3} {\mathrm e}^{-16} {\mathrm e}^{-\frac {16}{3}}\) | \(37\) |
default | \({\mathrm e}^{-\frac {16}{3}} {\mathrm e}^{-16} \left (-x^{8}-11 x^{7}-42 x^{6}-54 x^{5}+27 x^{4}+81 x^{3}\right )\) | \(41\) |
risch | \(-{\mathrm e}^{-\frac {64}{3}} x^{8}-11 \,{\mathrm e}^{-\frac {64}{3}} x^{7}-42 \,{\mathrm e}^{-\frac {64}{3}} x^{6}-54 \,{\mathrm e}^{-\frac {64}{3}} x^{5}+27 \,{\mathrm e}^{-\frac {64}{3}} x^{4}+81 \,{\mathrm e}^{-\frac {64}{3}} x^{3}\) | \(44\) |
norman | \(\left (81 \,{\mathrm e}^{-4} {\mathrm e}^{-\frac {4}{3}} x^{3}+27 \,{\mathrm e}^{-4} {\mathrm e}^{-\frac {4}{3}} x^{4}-54 \,{\mathrm e}^{-4} {\mathrm e}^{-\frac {4}{3}} x^{5}-42 \,{\mathrm e}^{-4} {\mathrm e}^{-\frac {4}{3}} x^{6}-11 \,{\mathrm e}^{-4} {\mathrm e}^{-\frac {4}{3}} x^{7}-{\mathrm e}^{-4} {\mathrm e}^{-\frac {4}{3}} x^{8}\right ) {\mathrm e}^{-12} {\mathrm e}^{-4}\) | \(89\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 33 vs.
\(2 (15) = 30\).
time = 0.27, size = 33, normalized size = 1.74 \begin {gather*} -{\left (x^{8} + 11 \, x^{7} + 42 \, x^{6} + 54 \, x^{5} - 27 \, x^{4} - 81 \, x^{3}\right )} e^{\left (-\frac {64}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 33 vs.
\(2 (15) = 30\).
time = 0.37, size = 33, normalized size = 1.74 \begin {gather*} -{\left (x^{8} + 11 \, x^{7} + 42 \, x^{6} + 54 \, x^{5} - 27 \, x^{4} - 81 \, x^{3}\right )} e^{\left (-\frac {64}{3}\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. 58 vs.
\(2 (15) = 30\).
time = 0.01, size = 58, normalized size = 3.05 \begin {gather*} - \frac {x^{8}}{e^{\frac {64}{3}}} - \frac {11 x^{7}}{e^{\frac {64}{3}}} - \frac {42 x^{6}}{e^{\frac {64}{3}}} - \frac {54 x^{5}}{e^{\frac {64}{3}}} + \frac {27 x^{4}}{e^{\frac {64}{3}}} + \frac {81 x^{3}}{e^{\frac {64}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 33 vs.
\(2 (15) = 30\).
time = 0.41, size = 33, normalized size = 1.74 \begin {gather*} -{\left (x^{8} + 11 \, x^{7} + 42 \, x^{6} + 54 \, x^{5} - 27 \, x^{4} - 81 \, x^{3}\right )} e^{\left (-\frac {64}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 43, normalized size = 2.26 \begin {gather*} -{\mathrm {e}}^{-\frac {64}{3}}\,x^8-11\,{\mathrm {e}}^{-\frac {64}{3}}\,x^7-42\,{\mathrm {e}}^{-\frac {64}{3}}\,x^6-54\,{\mathrm {e}}^{-\frac {64}{3}}\,x^5+27\,{\mathrm {e}}^{-\frac {64}{3}}\,x^4+81\,{\mathrm {e}}^{-\frac {64}{3}}\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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