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 = 0.01, antiderivative size = 39, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 39, normalized size = 1.00 \[ \frac {5 x^6}{6}-\frac {11 x^5}{5}-\frac {3 x^4}{4}+\frac {11 x^3}{3}+\frac {3 x^2}{2}-x \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 30, normalized size = 0.77 \[ \frac {1}{60} x \left (50 x^5-132 x^4-45 x^3+220 x^2+90 x-60\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 29, normalized size = 0.74 \[ \frac {5}{6} x^{6} - \frac {11}{5} x^{5} - \frac {3}{4} x^{4} + \frac {11}{3} x^{3} + \frac {3}{2} x^{2} - x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.58, size = 29, normalized size = 0.74 \[ \frac {5}{6} \, x^{6} - \frac {11}{5} \, x^{5} - \frac {3}{4} \, x^{4} + \frac {11}{3} \, x^{3} + \frac {3}{2} \, x^{2} - x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.36, size = 30, normalized size = 0.77
method | result | size |
gosper | \(-x +\frac {3}{2} x^{2}+\frac {11}{3} x^{3}-\frac {3}{4} x^{4}-\frac {11}{5} x^{5}+\frac {5}{6} x^{6}\) | \(30\) |
default | \(-x +\frac {3}{2} x^{2}+\frac {11}{3} x^{3}-\frac {3}{4} x^{4}-\frac {11}{5} x^{5}+\frac {5}{6} x^{6}\) | \(30\) |
norman | \(-x +\frac {3}{2} x^{2}+\frac {11}{3} x^{3}-\frac {3}{4} x^{4}-\frac {11}{5} x^{5}+\frac {5}{6} x^{6}\) | \(30\) |
risch | \(-x +\frac {3}{2} x^{2}+\frac {11}{3} x^{3}-\frac {3}{4} x^{4}-\frac {11}{5} x^{5}+\frac {5}{6} x^{6}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 29, normalized size = 0.74 \[ \frac {5}{6} \, x^{6} - \frac {11}{5} \, x^{5} - \frac {3}{4} \, x^{4} + \frac {11}{3} \, x^{3} + \frac {3}{2} \, x^{2} - x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 29, normalized size = 0.74 \[ \frac {5\,x^6}{6}-\frac {11\,x^5}{5}-\frac {3\,x^4}{4}+\frac {11\,x^3}{3}+\frac {3\,x^2}{2}-x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 34, normalized size = 0.87 \[ \frac {5 x^{6}}{6} - \frac {11 x^{5}}{5} - \frac {3 x^{4}}{4} + \frac {11 x^{3}}{3} + \frac {3 x^{2}}{2} - x \]
Verification of antiderivative is not currently implemented for this CAS.
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