Optimal. Leaf size=30 \[ \frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5} \]
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Rubi [A] time = 0.0099083, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^2 (a+b x)^2 \, dx &=\int \left (a^2 x^2+2 a b x^3+b^2 x^4\right ) \, dx\\ &=\frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5}\\ \end{align*}
Mathematica [A] time = 0.0029569, size = 30, normalized size = 1. \[ \frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 0.8 \begin{align*}{\frac{{a}^{2}{x}^{3}}{3}}+{\frac{ab{x}^{4}}{2}}+{\frac{{b}^{2}{x}^{5}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05648, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{5} \, b^{2} x^{5} + \frac{1}{2} \, a b x^{4} + \frac{1}{3} \, a^{2} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.35776, size = 55, normalized size = 1.83 \begin{align*} \frac{1}{5} x^{5} b^{2} + \frac{1}{2} x^{4} b a + \frac{1}{3} x^{3} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.075105, size = 24, normalized size = 0.8 \begin{align*} \frac{a^{2} x^{3}}{3} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{5}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1918, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{5} \, b^{2} x^{5} + \frac{1}{2} \, a b x^{4} + \frac{1}{3} \, a^{2} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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