Optimal. Leaf size=19 \[ \frac{1}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12} \]
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Rubi [A] time = 0.0054111, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {27, 43} \[ \frac{1}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12} \]
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin{align*} \int x (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x (1+x)^{11} \, dx\\ &=\int \left (-(1+x)^{11}+(1+x)^{12}\right ) \, dx\\ &=-\frac{1}{12} (1+x)^{12}+\frac{1}{13} (1+x)^{13}\\ \end{align*}
Mathematica [B] time = 0.0012607, size = 77, normalized size = 4.05 \[ \frac{x^{13}}{13}+\frac{11 x^{12}}{12}+5 x^{11}+\frac{33 x^{10}}{2}+\frac{110 x^9}{3}+\frac{231 x^8}{4}+66 x^7+55 x^6+33 x^5+\frac{55 x^4}{4}+\frac{11 x^3}{3}+\frac{x^2}{2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 62, normalized size = 3.3 \begin{align*}{\frac{{x}^{13}}{13}}+{\frac{11\,{x}^{12}}{12}}+5\,{x}^{11}+{\frac{33\,{x}^{10}}{2}}+{\frac{110\,{x}^{9}}{3}}+{\frac{231\,{x}^{8}}{4}}+66\,{x}^{7}+55\,{x}^{6}+33\,{x}^{5}+{\frac{55\,{x}^{4}}{4}}+{\frac{11\,{x}^{3}}{3}}+{\frac{{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.00792, size = 82, normalized size = 4.32 \begin{align*} \frac{1}{13} \, x^{13} + \frac{11}{12} \, x^{12} + 5 \, x^{11} + \frac{33}{2} \, x^{10} + \frac{110}{3} \, x^{9} + \frac{231}{4} \, x^{8} + 66 \, x^{7} + 55 \, x^{6} + 33 \, x^{5} + \frac{55}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{1}{2} \, x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.13056, size = 173, normalized size = 9.11 \begin{align*} \frac{1}{13} x^{13} + \frac{11}{12} x^{12} + 5 x^{11} + \frac{33}{2} x^{10} + \frac{110}{3} x^{9} + \frac{231}{4} x^{8} + 66 x^{7} + 55 x^{6} + 33 x^{5} + \frac{55}{4} x^{4} + \frac{11}{3} x^{3} + \frac{1}{2} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.07217, size = 70, normalized size = 3.68 \begin{align*} \frac{x^{13}}{13} + \frac{11 x^{12}}{12} + 5 x^{11} + \frac{33 x^{10}}{2} + \frac{110 x^{9}}{3} + \frac{231 x^{8}}{4} + 66 x^{7} + 55 x^{6} + 33 x^{5} + \frac{55 x^{4}}{4} + \frac{11 x^{3}}{3} + \frac{x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.1657, size = 82, normalized size = 4.32 \begin{align*} \frac{1}{13} \, x^{13} + \frac{11}{12} \, x^{12} + 5 \, x^{11} + \frac{33}{2} \, x^{10} + \frac{110}{3} \, x^{9} + \frac{231}{4} \, x^{8} + 66 \, x^{7} + 55 \, x^{6} + 33 \, x^{5} + \frac{55}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{1}{2} \, x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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