Optimal. Leaf size=60 \[ \frac{a x^{10}}{10}+\frac{3 a x^7}{7}+\frac{3 a x^4}{4}+a x+\frac{b x^{11}}{11}+\frac{3 b x^8}{8}+\frac{3 b x^5}{5}+\frac{b x^2}{2} \]
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Rubi [A] time = 0.037747, antiderivative size = 60, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {771} \[ \frac{a x^{10}}{10}+\frac{3 a x^7}{7}+\frac{3 a x^4}{4}+a x+\frac{b x^{11}}{11}+\frac{3 b x^8}{8}+\frac{3 b x^5}{5}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin{align*} \int (1+x)^3 (a+b x) \left (1-x+x^2\right )^3 \, dx &=\int \left (a+b x+3 a x^3+3 b x^4+3 a x^6+3 b x^7+a x^9+b x^{10}\right ) \, dx\\ &=a x+\frac{b x^2}{2}+\frac{3 a x^4}{4}+\frac{3 b x^5}{5}+\frac{3 a x^7}{7}+\frac{3 b x^8}{8}+\frac{a x^{10}}{10}+\frac{b x^{11}}{11}\\ \end{align*}
Mathematica [A] time = 0.00217, size = 60, normalized size = 1. \[ \frac{a x^{10}}{10}+\frac{3 a x^7}{7}+\frac{3 a x^4}{4}+a x+\frac{b x^{11}}{11}+\frac{3 b x^8}{8}+\frac{3 b x^5}{5}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 47, normalized size = 0.8 \begin{align*} ax+{\frac{b{x}^{2}}{2}}+{\frac{3\,a{x}^{4}}{4}}+{\frac{3\,b{x}^{5}}{5}}+{\frac{3\,a{x}^{7}}{7}}+{\frac{3\,b{x}^{8}}{8}}+{\frac{a{x}^{10}}{10}}+{\frac{b{x}^{11}}{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04165, size = 62, normalized size = 1.03 \begin{align*} \frac{1}{11} \, b x^{11} + \frac{1}{10} \, a x^{10} + \frac{3}{8} \, b x^{8} + \frac{3}{7} \, a x^{7} + \frac{3}{5} \, b x^{5} + \frac{3}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.11977, size = 126, normalized size = 2.1 \begin{align*} \frac{1}{11} x^{11} b + \frac{1}{10} x^{10} a + \frac{3}{8} x^{8} b + \frac{3}{7} x^{7} a + \frac{3}{5} x^{5} b + \frac{3}{4} x^{4} a + \frac{1}{2} x^{2} b + x a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.069017, size = 56, normalized size = 0.93 \begin{align*} \frac{a x^{10}}{10} + \frac{3 a x^{7}}{7} + \frac{3 a x^{4}}{4} + a x + \frac{b x^{11}}{11} + \frac{3 b x^{8}}{8} + \frac{3 b x^{5}}{5} + \frac{b x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13949, size = 62, normalized size = 1.03 \begin{align*} \frac{1}{11} \, b x^{11} + \frac{1}{10} \, a x^{10} + \frac{3}{8} \, b x^{8} + \frac{3}{7} \, a x^{7} + \frac{3}{5} \, b x^{5} + \frac{3}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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