Optimal. Leaf size=46 \[ \frac {4096 x^7}{7}-2048 x^9+\frac {34560 x^{11}}{11}-\frac {34560 x^{13}}{13}+1296 x^{15}-\frac {5832 x^{17}}{17}+\frac {729 x^{19}}{19} \]
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Rubi [A]
time = 0.01, 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 = {1607, 276}
\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 276
Rule 1607
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 {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 {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.38, size = 37, normalized size = 0.80
method | result | size |
default | \(\frac {4096}{7} x^{7}-2048 x^{9}+\frac {34560}{11} x^{11}-\frac {34560}{13} x^{13}+1296 x^{15}-\frac {5832}{17} x^{17}+\frac {729}{19} x^{19}\) | \(37\) |
norman | \(\frac {4096}{7} x^{7}-2048 x^{9}+\frac {34560}{11} x^{11}-\frac {34560}{13} x^{13}+1296 x^{15}-\frac {5832}{17} x^{17}+\frac {729}{19} x^{19}\) | \(37\) |
risch | \(\frac {4096}{7} x^{7}-2048 x^{9}+\frac {34560}{11} x^{11}-\frac {34560}{13} x^{13}+1296 x^{15}-\frac {5832}{17} x^{17}+\frac {729}{19} x^{19}\) | \(37\) |
gosper | \(\frac {x^{7} \left (12405393 x^{12}-110918808 x^{10}+419026608 x^{8}-859541760 x^{6}+1015822080 x^{4}-662165504 x^{2}+189190144\right )}{323323}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, 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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Fricas [A]
time = 2.27, 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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Sympy [A]
time = 0.01, 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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Giac [A]
time = 1.23, 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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