Optimal. Leaf size=46 \[ \frac {1}{16} (x+1)^{16}-\frac {4}{15} (x+1)^{15}+\frac {3}{7} (x+1)^{14}-\frac {4}{13} (x+1)^{13}+\frac {1}{12} (x+1)^{12} \]
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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 = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {27, 43} \[ \frac {1}{16} (x+1)^{16}-\frac {4}{15} (x+1)^{15}+\frac {3}{7} (x+1)^{14}-\frac {4}{13} (x+1)^{13}+\frac {1}{12} (x+1)^{12} \]
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin {align*} \int x^4 (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x^4 (1+x)^{11} \, dx\\ &=\int \left ((1+x)^{11}-4 (1+x)^{12}+6 (1+x)^{13}-4 (1+x)^{14}+(1+x)^{15}\right ) \, dx\\ &=\frac {1}{12} (1+x)^{12}-\frac {4}{13} (1+x)^{13}+\frac {3}{7} (1+x)^{14}-\frac {4}{15} (1+x)^{15}+\frac {1}{16} (1+x)^{16}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 83, normalized size = 1.80 \[ \frac {x^{16}}{16}+\frac {11 x^{15}}{15}+\frac {55 x^{14}}{14}+\frac {165 x^{13}}{13}+\frac {55 x^{12}}{2}+42 x^{11}+\frac {231 x^{10}}{5}+\frac {110 x^9}{3}+\frac {165 x^8}{8}+\frac {55 x^7}{7}+\frac {11 x^6}{6}+\frac {x^5}{5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 61, normalized size = 1.33 \[ \frac {1}{16} x^{16} + \frac {11}{15} x^{15} + \frac {55}{14} x^{14} + \frac {165}{13} x^{13} + \frac {55}{2} x^{12} + 42 x^{11} + \frac {231}{5} x^{10} + \frac {110}{3} x^{9} + \frac {165}{8} x^{8} + \frac {55}{7} x^{7} + \frac {11}{6} x^{6} + \frac {1}{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 61, normalized size = 1.33 \[ \frac {1}{16} \, x^{16} + \frac {11}{15} \, x^{15} + \frac {55}{14} \, x^{14} + \frac {165}{13} \, x^{13} + \frac {55}{2} \, x^{12} + 42 \, x^{11} + \frac {231}{5} \, x^{10} + \frac {110}{3} \, x^{9} + \frac {165}{8} \, x^{8} + \frac {55}{7} \, x^{7} + \frac {11}{6} \, x^{6} + \frac {1}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 62, normalized size = 1.35 \[ \frac {1}{16} x^{16}+\frac {11}{15} x^{15}+\frac {55}{14} x^{14}+\frac {165}{13} x^{13}+\frac {55}{2} x^{12}+42 x^{11}+\frac {231}{5} x^{10}+\frac {110}{3} x^{9}+\frac {165}{8} x^{8}+\frac {55}{7} x^{7}+\frac {11}{6} x^{6}+\frac {1}{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.69, size = 61, normalized size = 1.33 \[ \frac {1}{16} \, x^{16} + \frac {11}{15} \, x^{15} + \frac {55}{14} \, x^{14} + \frac {165}{13} \, x^{13} + \frac {55}{2} \, x^{12} + 42 \, x^{11} + \frac {231}{5} \, x^{10} + \frac {110}{3} \, x^{9} + \frac {165}{8} \, x^{8} + \frac {55}{7} \, x^{7} + \frac {11}{6} \, x^{6} + \frac {1}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 61, normalized size = 1.33 \[ \frac {x^{16}}{16}+\frac {11\,x^{15}}{15}+\frac {55\,x^{14}}{14}+\frac {165\,x^{13}}{13}+\frac {55\,x^{12}}{2}+42\,x^{11}+\frac {231\,x^{10}}{5}+\frac {110\,x^9}{3}+\frac {165\,x^8}{8}+\frac {55\,x^7}{7}+\frac {11\,x^6}{6}+\frac {x^5}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 75, normalized size = 1.63 \[ \frac {x^{16}}{16} + \frac {11 x^{15}}{15} + \frac {55 x^{14}}{14} + \frac {165 x^{13}}{13} + \frac {55 x^{12}}{2} + 42 x^{11} + \frac {231 x^{10}}{5} + \frac {110 x^{9}}{3} + \frac {165 x^{8}}{8} + \frac {55 x^{7}}{7} + \frac {11 x^{6}}{6} + \frac {x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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