Optimal. Leaf size=39 \[ \frac{5 x^6}{6}-\frac{11 x^5}{5}-\frac{3 x^4}{4}+\frac{11 x^3}{3}+\frac{3 x^2}{2}-x \]
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Rubi [A] time = 0.0141987, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {631} \[ \frac{5 x^6}{6}-\frac{11 x^5}{5}-\frac{3 x^4}{4}+\frac{11 x^3}{3}+\frac{3 x^2}{2}-x \]
Antiderivative was successfully verified.
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Rule 631
Rubi steps
\begin{align*} \int (-1+5 x) \left (-1-x+x^2\right )^2 \, dx &=\int \left (-1+3 x+11 x^2-3 x^3-11 x^4+5 x^5\right ) \, dx\\ &=-x+\frac{3 x^2}{2}+\frac{11 x^3}{3}-\frac{3 x^4}{4}-\frac{11 x^5}{5}+\frac{5 x^6}{6}\\ \end{align*}
Mathematica [A] time = 0.0013804, size = 39, normalized size = 1. \[ \frac{5 x^6}{6}-\frac{11 x^5}{5}-\frac{3 x^4}{4}+\frac{11 x^3}{3}+\frac{3 x^2}{2}-x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 30, normalized size = 0.8 \begin{align*} -x+{\frac{3\,{x}^{2}}{2}}+{\frac{11\,{x}^{3}}{3}}-{\frac{3\,{x}^{4}}{4}}-{\frac{11\,{x}^{5}}{5}}+{\frac{5\,{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.929819, size = 39, normalized size = 1. \begin{align*} \frac{5}{6} \, x^{6} - \frac{11}{5} \, x^{5} - \frac{3}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{3}{2} \, x^{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.75093, size = 74, normalized size = 1.9 \begin{align*} \frac{5}{6} x^{6} - \frac{11}{5} x^{5} - \frac{3}{4} x^{4} + \frac{11}{3} x^{3} + \frac{3}{2} x^{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.057382, size = 34, normalized size = 0.87 \begin{align*} \frac{5 x^{6}}{6} - \frac{11 x^{5}}{5} - \frac{3 x^{4}}{4} + \frac{11 x^{3}}{3} + \frac{3 x^{2}}{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06274, size = 39, normalized size = 1. \begin{align*} \frac{5}{6} \, x^{6} - \frac{11}{5} \, x^{5} - \frac{3}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{3}{2} \, x^{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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