Optimal. Leaf size=39 \[ \frac{3 x^6}{2}+\frac{3 x^5}{5}-\frac{7 x^4}{2}-\frac{2 x^3}{3}+\frac{5 x^2}{2}-x \]
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Rubi [A] time = 0.0157301, 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} \[ \frac{3 x^6}{2}+\frac{3 x^5}{5}-\frac{7 x^4}{2}-\frac{2 x^3}{3}+\frac{5 x^2}{2}-x \]
Antiderivative was successfully verified.
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Rule 631
Rubi steps
\begin{align*} \int (-1+x) \left (-1+2 x+3 x^2\right )^2 \, dx &=\int \left (-1+5 x-2 x^2-14 x^3+3 x^4+9 x^5\right ) \, dx\\ &=-x+\frac{5 x^2}{2}-\frac{2 x^3}{3}-\frac{7 x^4}{2}+\frac{3 x^5}{5}+\frac{3 x^6}{2}\\ \end{align*}
Mathematica [A] time = 0.0014211, size = 39, normalized size = 1. \[ \frac{3 x^6}{2}+\frac{3 x^5}{5}-\frac{7 x^4}{2}-\frac{2 x^3}{3}+\frac{5 x^2}{2}-x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 30, normalized size = 0.8 \begin{align*} -x+{\frac{5\,{x}^{2}}{2}}-{\frac{2\,{x}^{3}}{3}}-{\frac{7\,{x}^{4}}{2}}+{\frac{3\,{x}^{5}}{5}}+{\frac{3\,{x}^{6}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.931304, size = 39, normalized size = 1. \begin{align*} \frac{3}{2} \, x^{6} + \frac{3}{5} \, x^{5} - \frac{7}{2} \, x^{4} - \frac{2}{3} \, x^{3} + \frac{5}{2} \, x^{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59602, size = 72, normalized size = 1.85 \begin{align*} \frac{3}{2} x^{6} + \frac{3}{5} x^{5} - \frac{7}{2} x^{4} - \frac{2}{3} x^{3} + \frac{5}{2} x^{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058886, size = 34, normalized size = 0.87 \begin{align*} \frac{3 x^{6}}{2} + \frac{3 x^{5}}{5} - \frac{7 x^{4}}{2} - \frac{2 x^{3}}{3} + \frac{5 x^{2}}{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06343, size = 39, normalized size = 1. \begin{align*} \frac{3}{2} \, x^{6} + \frac{3}{5} \, x^{5} - \frac{7}{2} \, x^{4} - \frac{2}{3} \, x^{3} + \frac{5}{2} \, x^{2} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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