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 = 0.0138082, antiderivative size = 28, normalized size of antiderivative = 1., 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} \[ \frac{1}{14} (x+1)^{14}-\frac{2}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12} \]
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin{align*} \int x^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*}
Mathematica [B] time = 0.001437, size = 79, normalized size = 2.82 \[ \frac{x^{14}}{14}+\frac{11 x^{13}}{13}+\frac{55 x^{12}}{12}+15 x^{11}+33 x^{10}+\frac{154 x^9}{3}+\frac{231 x^8}{4}+\frac{330 x^7}{7}+\frac{55 x^6}{2}+11 x^5+\frac{11 x^4}{4}+\frac{x^3}{3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 62, normalized size = 2.2 \begin{align*}{\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.957947, size = 82, normalized size = 2.93 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.13238, size = 181, normalized size = 6.46 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.072574, size = 71, normalized size = 2.54 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.11318, size = 82, normalized size = 2.93 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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