Optimal. Leaf size=23 \[ \frac {2}{15} (x+1)^{5/2} \left (x^2-x+1\right )^{5/2} \]
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Rubi [A] time = 0.02, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {913} \[ \frac {2}{15} (x+1)^{5/2} \left (x^2-x+1\right )^{5/2} \]
Antiderivative was successfully verified.
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Rule 913
Rubi steps
\begin {align*} \int x^2 (1+x)^{3/2} \left (1-x+x^2\right )^{3/2} \, dx &=\frac {2}{15} (1+x)^{5/2} \left (1-x+x^2\right )^{5/2}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 23, normalized size = 1.00 \[ \frac {2}{15} (x+1)^{5/2} \left (x^2-x+1\right )^{5/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.09, size = 27, normalized size = 1.17 \[ \frac {2}{15} \, {\left (x^{6} + 2 \, x^{3} + 1\right )} \sqrt {x^{2} - x + 1} \sqrt {x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.61, size = 173, normalized size = 7.52 \[ \frac {2}{45045} \, {\left ({\left ({\left (7 \, {\left (3 \, {\left (11 \, {\left (13 \, x - 80\right )} {\left (x + 1\right )} + 3165\right )} {\left (x + 1\right )} - 16442\right )} {\left (x + 1\right )} + 121227\right )} {\left (x + 1\right )} - 80187\right )} {\left (x + 1\right )} + 34077\right )} \sqrt {{\left (x + 1\right )}^{2} - 3 \, x} \sqrt {x + 1} + \frac {2}{45045} \, {\left ({\left (5 \, {\left (7 \, {\left (9 \, {\left (11 \, x - 57\right )} {\left (x + 1\right )} + 1601\right )} {\left (x + 1\right )} - 15837\right )} {\left (x + 1\right )} + 65172\right )} {\left (x + 1\right )} - 34077\right )} \sqrt {{\left (x + 1\right )}^{2} - 3 \, x} \sqrt {x + 1} + \frac {2}{315} \, {\left ({\left (5 \, {\left (7 \, x - 23\right )} {\left (x + 1\right )} + 258\right )} {\left (x + 1\right )} - 213\right )} \sqrt {{\left (x + 1\right )}^{2} - 3 \, x} \sqrt {x + 1} + \frac {2}{105} \, {\left (3 \, {\left (5 \, x - 12\right )} {\left (x + 1\right )} + 71\right )} \sqrt {{\left (x + 1\right )}^{2} - 3 \, x} \sqrt {x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.78 \[ \frac {2 \left (x +1\right )^{\frac {5}{2}} \left (x^{2}-x +1\right )^{\frac {5}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.97, size = 27, normalized size = 1.17 \[ \frac {2}{15} \, {\left (x^{6} + 2 \, x^{3} + 1\right )} \sqrt {x^{2} - x + 1} \sqrt {x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 25, normalized size = 1.09 \[ \frac {2\,\sqrt {x+1}\,{\left (x^2-x+1\right )}^{5/2}\,\left (x^2+2\,x+1\right )}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{2} \left (x + 1\right )^{\frac {3}{2}} \left (x^{2} - x + 1\right )^{\frac {3}{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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