Optimal. Leaf size=37 \[ \frac {1}{15} (x+1)^{15}-\frac {3}{14} (x+1)^{14}+\frac {3}{13} (x+1)^{13}-\frac {1}{12} (x+1)^{12} \]
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Rubi [A] time = 0.02, antiderivative size = 37, 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} \begin {gather*} \frac {1}{15} (x+1)^{15}-\frac {3}{14} (x+1)^{14}+\frac {3}{13} (x+1)^{13}-\frac {1}{12} (x+1)^{12} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin {align*} \int x^3 (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x^3 (1+x)^{11} \, dx\\ &=\int \left (-(1+x)^{11}+3 (1+x)^{12}-3 (1+x)^{13}+(1+x)^{14}\right ) \, dx\\ &=-\frac {1}{12} (1+x)^{12}+\frac {3}{13} (1+x)^{13}-\frac {3}{14} (1+x)^{14}+\frac {1}{15} (1+x)^{15}\\ \end {align*}
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Mathematica [B] time = 0.00, size = 83, normalized size = 2.24 \begin {gather*} \frac {x^{15}}{15}+\frac {11 x^{14}}{14}+\frac {55 x^{13}}{13}+\frac {55 x^{12}}{4}+30 x^{11}+\frac {231 x^{10}}{5}+\frac {154 x^9}{3}+\frac {165 x^8}{4}+\frac {165 x^7}{7}+\frac {55 x^6}{6}+\frac {11 x^5}{5}+\frac {x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^3 (1+x) \left (1+2 x+x^2\right )^5 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.35, size = 61, normalized size = 1.65 \begin {gather*} \frac {1}{15} x^{15} + \frac {11}{14} x^{14} + \frac {55}{13} x^{13} + \frac {55}{4} x^{12} + 30 x^{11} + \frac {231}{5} x^{10} + \frac {154}{3} x^{9} + \frac {165}{4} x^{8} + \frac {165}{7} x^{7} + \frac {55}{6} x^{6} + \frac {11}{5} x^{5} + \frac {1}{4} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 61, normalized size = 1.65 \begin {gather*} \frac {1}{15} \, x^{15} + \frac {11}{14} \, x^{14} + \frac {55}{13} \, x^{13} + \frac {55}{4} \, x^{12} + 30 \, x^{11} + \frac {231}{5} \, x^{10} + \frac {154}{3} \, x^{9} + \frac {165}{4} \, x^{8} + \frac {165}{7} \, x^{7} + \frac {55}{6} \, x^{6} + \frac {11}{5} \, x^{5} + \frac {1}{4} \, x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 62, normalized size = 1.68 \begin {gather*} \frac {1}{15} x^{15}+\frac {11}{14} x^{14}+\frac {55}{13} x^{13}+\frac {55}{4} x^{12}+30 x^{11}+\frac {231}{5} x^{10}+\frac {154}{3} x^{9}+\frac {165}{4} x^{8}+\frac {165}{7} x^{7}+\frac {55}{6} x^{6}+\frac {11}{5} x^{5}+\frac {1}{4} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.60, size = 61, normalized size = 1.65 \begin {gather*} \frac {1}{15} \, x^{15} + \frac {11}{14} \, x^{14} + \frac {55}{13} \, x^{13} + \frac {55}{4} \, x^{12} + 30 \, x^{11} + \frac {231}{5} \, x^{10} + \frac {154}{3} \, x^{9} + \frac {165}{4} \, x^{8} + \frac {165}{7} \, x^{7} + \frac {55}{6} \, x^{6} + \frac {11}{5} \, x^{5} + \frac {1}{4} \, x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 61, normalized size = 1.65 \begin {gather*} \frac {x^{15}}{15}+\frac {11\,x^{14}}{14}+\frac {55\,x^{13}}{13}+\frac {55\,x^{12}}{4}+30\,x^{11}+\frac {231\,x^{10}}{5}+\frac {154\,x^9}{3}+\frac {165\,x^8}{4}+\frac {165\,x^7}{7}+\frac {55\,x^6}{6}+\frac {11\,x^5}{5}+\frac {x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 75, normalized size = 2.03 \begin {gather*} \frac {x^{15}}{15} + \frac {11 x^{14}}{14} + \frac {55 x^{13}}{13} + \frac {55 x^{12}}{4} + 30 x^{11} + \frac {231 x^{10}}{5} + \frac {154 x^{9}}{3} + \frac {165 x^{8}}{4} + \frac {165 x^{7}}{7} + \frac {55 x^{6}}{6} + \frac {11 x^{5}}{5} + \frac {x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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