Optimal. Leaf size=44 \[ \frac{a x^7}{7}+\frac{a x^4}{2}+a x+\frac{b x^8}{8}+\frac{2 b x^5}{5}+\frac{b x^2}{2} \]
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Rubi [A] time = 0.0283479, antiderivative size = 44, 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} \[ \frac{a x^7}{7}+\frac{a x^4}{2}+a x+\frac{b x^8}{8}+\frac{2 b x^5}{5}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin{align*} \int (1+x)^2 (a+b x) \left (1-x+x^2\right )^2 \, dx &=\int \left (a+b x+2 a x^3+2 b x^4+a x^6+b x^7\right ) \, dx\\ &=a x+\frac{b x^2}{2}+\frac{a x^4}{2}+\frac{2 b x^5}{5}+\frac{a x^7}{7}+\frac{b x^8}{8}\\ \end{align*}
Mathematica [A] time = 0.0017215, size = 44, normalized size = 1. \[ \frac{a x^7}{7}+\frac{a x^4}{2}+a x+\frac{b x^8}{8}+\frac{2 b x^5}{5}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 35, normalized size = 0.8 \begin{align*} ax+{\frac{b{x}^{2}}{2}}+{\frac{a{x}^{4}}{2}}+{\frac{2\,b{x}^{5}}{5}}+{\frac{a{x}^{7}}{7}}+{\frac{b{x}^{8}}{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00216, size = 46, normalized size = 1.05 \begin{align*} \frac{1}{8} \, b x^{8} + \frac{1}{7} \, a x^{7} + \frac{2}{5} \, b x^{5} + \frac{1}{2} \, 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 = 1.03459, size = 88, normalized size = 2. \begin{align*} \frac{1}{8} x^{8} b + \frac{1}{7} x^{7} a + \frac{2}{5} x^{5} b + \frac{1}{2} 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 = 0.062244, size = 37, normalized size = 0.84 \begin{align*} \frac{a x^{7}}{7} + \frac{a x^{4}}{2} + a x + \frac{b x^{8}}{8} + \frac{2 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 = 1.0932, size = 46, normalized size = 1.05 \begin{align*} \frac{1}{8} \, b x^{8} + \frac{1}{7} \, a x^{7} + \frac{2}{5} \, b x^{5} + \frac{1}{2} \, 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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