Optimal. Leaf size=28 \[ \frac {1}{14} (x+1)^{14}-\frac {2}{13} (x+1)^{13}+\frac {1}{12} (x+1)^{12} \]
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Rubi [A] time = 0.01, antiderivative size = 28, 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}{14} (x+1)^{14}-\frac {2}{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^2 (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x^2 (1+x)^{11} \, dx\\ &=\int \left ((1+x)^{11}-2 (1+x)^{12}+(1+x)^{13}\right ) \, dx\\ &=\frac {1}{12} (1+x)^{12}-\frac {2}{13} (1+x)^{13}+\frac {1}{14} (1+x)^{14}\\ \end {align*}
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Mathematica [B] time = 0.00, size = 79, normalized size = 2.82 \begin {gather*} \frac {x^{14}}{14}+\frac {11 x^{13}}{13}+\frac {55 x^{12}}{12}+15 x^{11}+33 x^{10}+\frac {154 x^9}{3}+\frac {231 x^8}{4}+\frac {330 x^7}{7}+\frac {55 x^6}{2}+11 x^5+\frac {11 x^4}{4}+\frac {x^3}{3} \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^2 (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 = 0.34, size = 61, normalized size = 2.18 \begin {gather*} \frac {1}{14} x^{14} + \frac {11}{13} x^{13} + \frac {55}{12} x^{12} + 15 x^{11} + 33 x^{10} + \frac {154}{3} x^{9} + \frac {231}{4} x^{8} + \frac {330}{7} x^{7} + \frac {55}{2} x^{6} + 11 x^{5} + \frac {11}{4} x^{4} + \frac {1}{3} x^{3} \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 = 2.18 \begin {gather*} \frac {1}{14} \, x^{14} + \frac {11}{13} \, x^{13} + \frac {55}{12} \, x^{12} + 15 \, x^{11} + 33 \, x^{10} + \frac {154}{3} \, x^{9} + \frac {231}{4} \, x^{8} + \frac {330}{7} \, x^{7} + \frac {55}{2} \, x^{6} + 11 \, x^{5} + \frac {11}{4} \, x^{4} + \frac {1}{3} \, x^{3} \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 = 2.21 \begin {gather*} \frac {1}{14} x^{14}+\frac {11}{13} x^{13}+\frac {55}{12} x^{12}+15 x^{11}+33 x^{10}+\frac {154}{3} x^{9}+\frac {231}{4} x^{8}+\frac {330}{7} x^{7}+\frac {55}{2} x^{6}+11 x^{5}+\frac {11}{4} x^{4}+\frac {1}{3} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.61, size = 61, normalized size = 2.18 \begin {gather*} \frac {1}{14} \, x^{14} + \frac {11}{13} \, x^{13} + \frac {55}{12} \, x^{12} + 15 \, x^{11} + 33 \, x^{10} + \frac {154}{3} \, x^{9} + \frac {231}{4} \, x^{8} + \frac {330}{7} \, x^{7} + \frac {55}{2} \, x^{6} + 11 \, x^{5} + \frac {11}{4} \, x^{4} + \frac {1}{3} \, x^{3} \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 = 2.18 \begin {gather*} \frac {x^{14}}{14}+\frac {11\,x^{13}}{13}+\frac {55\,x^{12}}{12}+15\,x^{11}+33\,x^{10}+\frac {154\,x^9}{3}+\frac {231\,x^8}{4}+\frac {330\,x^7}{7}+\frac {55\,x^6}{2}+11\,x^5+\frac {11\,x^4}{4}+\frac {x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 71, normalized size = 2.54 \begin {gather*} \frac {x^{14}}{14} + \frac {11 x^{13}}{13} + \frac {55 x^{12}}{12} + 15 x^{11} + 33 x^{10} + \frac {154 x^{9}}{3} + \frac {231 x^{8}}{4} + \frac {330 x^{7}}{7} + \frac {55 x^{6}}{2} + 11 x^{5} + \frac {11 x^{4}}{4} + \frac {x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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