Optimal. Leaf size=23 \[ -\frac {2}{9 (x+1)^{3/2} \left (x^2-x+1\right )^{3/2}} \]
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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} \[ -\frac {2}{9 (x+1)^{3/2} \left (x^2-x+1\right )^{3/2}} \]
Antiderivative was successfully verified.
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Rule 913
Rubi steps
\begin {align*} \int \frac {x^2}{(1+x)^{5/2} \left (1-x+x^2\right )^{5/2}} \, dx &=-\frac {2}{9 (1+x)^{3/2} \left (1-x+x^2\right )^{3/2}}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 23, normalized size = 1.00 \[ -\frac {2}{9 (x+1)^{3/2} \left (x^2-x+1\right )^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 29, normalized size = 1.26 \[ -\frac {2 \, \sqrt {x^{2} - x + 1} \sqrt {x + 1}}{9 \, {\left (x^{6} + 2 \, x^{3} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{{\left (x^{2} - x + 1\right )}^{\frac {5}{2}} {\left (x + 1\right )}^{\frac {5}{2}}}\,{d x} \]
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 \[ -\frac {2}{9 \left (x +1\right )^{\frac {3}{2}} \left (x^{2}-x +1\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.97, size = 24, normalized size = 1.04 \[ -\frac {2}{9 \, {\left (x^{3} + 1\right )} \sqrt {x^{2} - x + 1} \sqrt {x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.88, size = 82, normalized size = 3.57 \[ \frac {18\,\sqrt {x+1}\,{\left (x^2-x+1\right )}^{5/2}-18\,x\,\sqrt {x+1}\,{\left (x^2-x+1\right )}^{5/2}}{\left (x+1\right )\,\left (81\,x\,{\left (x^2-x+1\right )}^4-162\,{\left (x^2-x+1\right )}^4+81\,{\left (x^2-x+1\right )}^5\right )} \]
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 \[ \int \frac {x^{2}}{\left (x + 1\right )^{\frac {5}{2}} \left (x^{2} - x + 1\right )^{\frac {5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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