Optimal. Leaf size=36 \[ 3-\frac {1}{5} x \left (\frac {3}{e^3}+\frac {1}{16} x^4 (5+2 x)^2 \left (-x+x^2\right )^2\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 44, normalized size of antiderivative = 1.22, number of steps
used = 3, number of rules used = 1, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {12}
\begin {gather*} -\frac {x^{11}}{20}-\frac {3 x^{10}}{20}+\frac {11 x^9}{80}+\frac {3 x^8}{8}-\frac {5 x^7}{16}-\frac {3 x}{5 e^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-48+e^3 \left (-175 x^6+240 x^7+99 x^8-120 x^9-44 x^{10}\right )\right ) \, dx}{80 e^3}\\ &=-\frac {3 x}{5 e^3}+\frac {1}{80} \int \left (-175 x^6+240 x^7+99 x^8-120 x^9-44 x^{10}\right ) \, dx\\ &=-\frac {3 x}{5 e^3}-\frac {5 x^7}{16}+\frac {3 x^8}{8}+\frac {11 x^9}{80}-\frac {3 x^{10}}{20}-\frac {x^{11}}{20}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 44, normalized size = 1.22 \begin {gather*} -\frac {3 x}{5 e^3}-\frac {5 x^7}{16}+\frac {3 x^8}{8}+\frac {11 x^9}{80}-\frac {3 x^{10}}{20}-\frac {x^{11}}{20} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 46, normalized size = 1.28
method | result | size |
risch | \(-\frac {5 x^{7}}{16}+\frac {3 x^{8}}{8}+\frac {11 x^{9}}{80}-\frac {3 x^{10}}{20}-\frac {x^{11}}{20}-\frac {3 x \,{\mathrm e}^{-3}}{5}\) | \(32\) |
norman | \(-\frac {5 x^{7}}{16}+\frac {3 x^{8}}{8}+\frac {11 x^{9}}{80}-\frac {3 x^{10}}{20}-\frac {x^{11}}{20}-\frac {3 x \,{\mathrm e}^{-3}}{5}\) | \(34\) |
gosper | \(-\frac {x \left (4 \,{\mathrm e}^{3} x^{10}+12 \,{\mathrm e}^{3} x^{9}-11 \,{\mathrm e}^{3} x^{8}-30 x^{7} {\mathrm e}^{3}+25 x^{6} {\mathrm e}^{3}+48\right ) {\mathrm e}^{-3}}{80}\) | \(45\) |
default | \(\frac {{\mathrm e}^{-3} \left (-4 \,{\mathrm e}^{3} x^{11}-12 \,{\mathrm e}^{3} x^{10}+11 \,{\mathrm e}^{3} x^{9}+30 \,{\mathrm e}^{3} x^{8}-25 x^{7} {\mathrm e}^{3}-48 x \right )}{80}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 37, normalized size = 1.03 \begin {gather*} -\frac {1}{80} \, {\left ({\left (4 \, x^{11} + 12 \, x^{10} - 11 \, x^{9} - 30 \, x^{8} + 25 \, x^{7}\right )} e^{3} + 48 \, x\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 37, normalized size = 1.03 \begin {gather*} -\frac {1}{80} \, {\left ({\left (4 \, x^{11} + 12 \, x^{10} - 11 \, x^{9} - 30 \, x^{8} + 25 \, x^{7}\right )} e^{3} + 48 \, x\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 39, normalized size = 1.08 \begin {gather*} - \frac {x^{11}}{20} - \frac {3 x^{10}}{20} + \frac {11 x^{9}}{80} + \frac {3 x^{8}}{8} - \frac {5 x^{7}}{16} - \frac {3 x}{5 e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 37, normalized size = 1.03 \begin {gather*} -\frac {1}{80} \, {\left ({\left (4 \, x^{11} + 12 \, x^{10} - 11 \, x^{9} - 30 \, x^{8} + 25 \, x^{7}\right )} e^{3} + 48 \, x\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 31, normalized size = 0.86 \begin {gather*} -\frac {x^{11}}{20}-\frac {3\,x^{10}}{20}+\frac {11\,x^9}{80}+\frac {3\,x^8}{8}-\frac {5\,x^7}{16}-\frac {3\,{\mathrm {e}}^{-3}\,x}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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