Optimal. Leaf size=30 \[ \frac{a^2 x^2}{2}+\frac{1}{3} a b x^6+\frac{b^2 x^{10}}{10} \]
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Rubi [A] time = 0.0091989, 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 = {270} \[ \frac{a^2 x^2}{2}+\frac{1}{3} a b x^6+\frac{b^2 x^{10}}{10} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin{align*} \int x \left (a+b x^4\right )^2 \, dx &=\int \left (a^2 x+2 a b x^5+b^2 x^9\right ) \, dx\\ &=\frac{a^2 x^2}{2}+\frac{1}{3} a b x^6+\frac{b^2 x^{10}}{10}\\ \end{align*}
Mathematica [A] time = 0.0015527, size = 30, normalized size = 1. \[ \frac{a^2 x^2}{2}+\frac{1}{3} a b x^6+\frac{b^2 x^{10}}{10} \]
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}^{2}}{2}}+{\frac{ab{x}^{6}}{3}}+{\frac{{b}^{2}{x}^{10}}{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959697, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{10} \, b^{2} x^{10} + \frac{1}{3} \, a b x^{6} + \frac{1}{2} \, a^{2} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.30261, size = 58, normalized size = 1.93 \begin{align*} \frac{1}{10} x^{10} b^{2} + \frac{1}{3} x^{6} b a + \frac{1}{2} x^{2} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.077956, size = 24, normalized size = 0.8 \begin{align*} \frac{a^{2} x^{2}}{2} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{10}}{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08223, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{10} \, b^{2} x^{10} + \frac{1}{3} \, a b x^{6} + \frac{1}{2} \, a^{2} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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