Optimal. Leaf size=22 \[ a^2 x+a b x^2+\frac{b^2 x^3}{3} \]
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Rubi [A] time = 0.004962, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a^2 x+a b x^2+\frac{b^2 x^3}{3} \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (a^2+2 a b x+b^2 x^2\right ) \, dx &=a^2 x+a b x^2+\frac{b^2 x^3}{3}\\ \end{align*}
Mathematica [A] time = 0.0000511, size = 22, normalized size = 1. \[ a^2 x+a b x^2+\frac{b^2 x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.038, size = 21, normalized size = 1. \begin{align*}{a}^{2}x+ab{x}^{2}+{\frac{{b}^{2}{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.17979, size = 27, normalized size = 1.23 \begin{align*} \frac{1}{3} \, b^{2} x^{3} + a b x^{2} + a^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.64184, size = 42, normalized size = 1.91 \begin{align*} \frac{1}{3} x^{3} b^{2} + x^{2} b a + x a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.064795, size = 19, normalized size = 0.86 \begin{align*} a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11468, size = 27, normalized size = 1.23 \begin{align*} \frac{1}{3} \, b^{2} x^{3} + a b x^{2} + a^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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