Optimal. Leaf size=9 \[ \frac{1}{12} (x+1)^{12} \]
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Rubi [A] time = 0.001211, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {27, 32} \[ \frac{1}{12} (x+1)^{12} \]
Antiderivative was successfully verified.
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Rule 27
Rule 32
Rubi steps
\begin{align*} \int (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int (1+x)^{11} \, dx\\ &=\frac{1}{12} (1+x)^{12}\\ \end{align*}
Mathematica [A] time = 0.0011257, size = 9, normalized size = 1. \[ \frac{1}{12} (x+1)^{12} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 56, normalized size = 6.2 \begin{align*}{\frac{{x}^{12}}{12}}+{x}^{11}+{\frac{11\,{x}^{10}}{2}}+{\frac{55\,{x}^{9}}{3}}+{\frac{165\,{x}^{8}}{4}}+66\,{x}^{7}+77\,{x}^{6}+66\,{x}^{5}+{\frac{165\,{x}^{4}}{4}}+{\frac{55\,{x}^{3}}{3}}+{\frac{11\,{x}^{2}}{2}}+x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01466, size = 16, normalized size = 1.78 \begin{align*} \frac{1}{12} \,{\left (x^{2} + 2 \, x + 1\right )}^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.15764, size = 159, normalized size = 17.67 \begin{align*} \frac{1}{12} x^{12} + x^{11} + \frac{11}{2} x^{10} + \frac{55}{3} x^{9} + \frac{165}{4} x^{8} + 66 x^{7} + 77 x^{6} + 66 x^{5} + \frac{165}{4} x^{4} + \frac{55}{3} x^{3} + \frac{11}{2} x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.105322, size = 65, normalized size = 7.22 \begin{align*} \frac{x^{12}}{12} + x^{11} + \frac{11 x^{10}}{2} + \frac{55 x^{9}}{3} + \frac{165 x^{8}}{4} + 66 x^{7} + 77 x^{6} + 66 x^{5} + \frac{165 x^{4}}{4} + \frac{55 x^{3}}{3} + \frac{11 x^{2}}{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.11678, size = 74, normalized size = 8.22 \begin{align*} \frac{1}{12} \, x^{12} + x^{11} + \frac{11}{2} \, x^{10} + \frac{55}{3} \, x^{9} + \frac{165}{4} \, x^{8} + 66 \, x^{7} + 77 \, x^{6} + 66 \, x^{5} + \frac{165}{4} \, x^{4} + \frac{55}{3} \, x^{3} + \frac{11}{2} \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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