Optimal. Leaf size=30 \[ \frac{a^2 x^5}{5}+\frac{1}{3} a b x^6+\frac{b^2 x^7}{7} \]
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Rubi [A] time = 0.0134057, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {1593, 43} \[ \frac{a^2 x^5}{5}+\frac{1}{3} a b x^6+\frac{b^2 x^7}{7} \]
Antiderivative was successfully verified.
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Rule 1593
Rule 43
Rubi steps
\begin{align*} \int \left (a x^2+b x^3\right )^2 \, dx &=\int x^4 (a+b x)^2 \, dx\\ &=\int \left (a^2 x^4+2 a b x^5+b^2 x^6\right ) \, dx\\ &=\frac{a^2 x^5}{5}+\frac{1}{3} a b x^6+\frac{b^2 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0015421, size = 30, normalized size = 1. \[ \frac{a^2 x^5}{5}+\frac{1}{3} a b x^6+\frac{b^2 x^7}{7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 25, normalized size = 0.8 \begin{align*}{\frac{{a}^{2}{x}^{5}}{5}}+{\frac{ab{x}^{6}}{3}}+{\frac{{b}^{2}{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.993275, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{7} \, b^{2} x^{7} + \frac{1}{3} \, a b x^{6} + \frac{1}{5} \, a^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.626779, size = 55, normalized size = 1.83 \begin{align*} \frac{1}{7} x^{7} b^{2} + \frac{1}{3} x^{6} b a + \frac{1}{5} x^{5} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.122, size = 24, normalized size = 0.8 \begin{align*} \frac{a^{2} x^{5}}{5} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15384, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{7} \, b^{2} x^{7} + \frac{1}{3} \, a b x^{6} + \frac{1}{5} \, a^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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