Optimal. Leaf size=23 \[ \frac{2}{3} \sqrt{x+1} \sqrt{x^2-x+1} \]
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Rubi [A] time = 0.0187211, antiderivative size = 23, normalized size of antiderivative = 1., 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} \[ \frac{2}{3} \sqrt{x+1} \sqrt{x^2-x+1} \]
Antiderivative was successfully verified.
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Rule 913
Rubi steps
\begin{align*} \int \frac{x^2}{\sqrt{1+x} \sqrt{1-x+x^2}} \, dx &=\frac{2}{3} \sqrt{1+x} \sqrt{1-x+x^2}\\ \end{align*}
Mathematica [A] time = 0.0255489, size = 23, normalized size = 1. \[ \frac{2}{3} \sqrt{x+1} \sqrt{x^2-x+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 18, normalized size = 0.8 \begin{align*}{\frac{2}{3}\sqrt{1+x}\sqrt{{x}^{2}-x+1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.47163, size = 30, normalized size = 1.3 \begin{align*} \frac{2 \,{\left (x^{3} + 1\right )}}{3 \, \sqrt{x^{2} - x + 1} \sqrt{x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68422, size = 47, normalized size = 2.04 \begin{align*} \frac{2}{3} \, \sqrt{x^{2} - x + 1} \sqrt{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{2}}{\sqrt{x + 1} \sqrt{x^{2} - x + 1}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17004, size = 24, normalized size = 1.04 \begin{align*} \frac{2}{3} \, \sqrt{{\left (x + 1\right )}^{2} - 3 \, x} \sqrt{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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