Optimal. Leaf size=46 \[ \frac {729 x^{19}}{19}-\frac {5832 x^{17}}{17}+1296 x^{15}-\frac {34560 x^{13}}{13}+\frac {34560 x^{11}}{11}-2048 x^9+\frac {4096 x^7}{7} \]
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Rubi [A] time = 0.02, antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1593, 270} \begin {gather*} \frac {729 x^{19}}{19}-\frac {5832 x^{17}}{17}+1296 x^{15}-\frac {34560 x^{13}}{13}+\frac {34560 x^{11}}{11}-2048 x^9+\frac {4096 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rule 1593
Rubi steps
\begin {align*} \int \left (-4 x+3 x^3\right )^6 \, dx &=\int x^6 \left (-4+3 x^2\right )^6 \, dx\\ &=\int \left (4096 x^6-18432 x^8+34560 x^{10}-34560 x^{12}+19440 x^{14}-5832 x^{16}+729 x^{18}\right ) \, dx\\ &=\frac {4096 x^7}{7}-2048 x^9+\frac {34560 x^{11}}{11}-\frac {34560 x^{13}}{13}+1296 x^{15}-\frac {5832 x^{17}}{17}+\frac {729 x^{19}}{19}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 46, normalized size = 1.00 \begin {gather*} \frac {729 x^{19}}{19}-\frac {5832 x^{17}}{17}+1296 x^{15}-\frac {34560 x^{13}}{13}+\frac {34560 x^{11}}{11}-2048 x^9+\frac {4096 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (-4 x+3 x^3\right )^6 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.35, size = 36, normalized size = 0.78 \begin {gather*} \frac {729}{19} x^{19} - \frac {5832}{17} x^{17} + 1296 x^{15} - \frac {34560}{13} x^{13} + \frac {34560}{11} x^{11} - 2048 x^{9} + \frac {4096}{7} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 36, normalized size = 0.78 \begin {gather*} \frac {729}{19} \, x^{19} - \frac {5832}{17} \, x^{17} + 1296 \, x^{15} - \frac {34560}{13} \, x^{13} + \frac {34560}{11} \, x^{11} - 2048 \, x^{9} + \frac {4096}{7} \, x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 37, normalized size = 0.80 \begin {gather*} \frac {729}{19} x^{19}-\frac {5832}{17} x^{17}+1296 x^{15}-\frac {34560}{13} x^{13}+\frac {34560}{11} x^{11}-2048 x^{9}+\frac {4096}{7} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 36, normalized size = 0.78 \begin {gather*} \frac {729}{19} \, x^{19} - \frac {5832}{17} \, x^{17} + 1296 \, x^{15} - \frac {34560}{13} \, x^{13} + \frac {34560}{11} \, x^{11} - 2048 \, x^{9} + \frac {4096}{7} \, x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 36, normalized size = 0.78 \begin {gather*} \frac {729\,x^{19}}{19}-\frac {5832\,x^{17}}{17}+1296\,x^{15}-\frac {34560\,x^{13}}{13}+\frac {34560\,x^{11}}{11}-2048\,x^9+\frac {4096\,x^7}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 42, normalized size = 0.91 \begin {gather*} \frac {729 x^{19}}{19} - \frac {5832 x^{17}}{17} + 1296 x^{15} - \frac {34560 x^{13}}{13} + \frac {34560 x^{11}}{11} - 2048 x^{9} + \frac {4096 x^{7}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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