Optimal. Leaf size=35 \[ a^2 c x^3+a^3 x+\frac{3}{5} a c^2 x^5+\frac{c^3 x^7}{7} \]
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Rubi [A] time = 0.0114554, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {194} \[ a^2 c x^3+a^3 x+\frac{3}{5} a c^2 x^5+\frac{c^3 x^7}{7} \]
Antiderivative was successfully verified.
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Rule 194
Rubi steps
\begin{align*} \int \left (a+c x^2\right )^3 \, dx &=\int \left (a^3+3 a^2 c x^2+3 a c^2 x^4+c^3 x^6\right ) \, dx\\ &=a^3 x+a^2 c x^3+\frac{3}{5} a c^2 x^5+\frac{c^3 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0012346, size = 35, normalized size = 1. \[ a^2 c x^3+a^3 x+\frac{3}{5} a c^2 x^5+\frac{c^3 x^7}{7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.046, size = 32, normalized size = 0.9 \begin{align*} x{a}^{3}+{a}^{2}c{x}^{3}+{\frac{3\,a{c}^{2}{x}^{5}}{5}}+{\frac{{c}^{3}{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.14035, size = 42, normalized size = 1.2 \begin{align*} \frac{1}{7} \, c^{3} x^{7} + \frac{3}{5} \, a c^{2} x^{5} + a^{2} c x^{3} + a^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.85996, size = 66, normalized size = 1.89 \begin{align*} \frac{1}{7} x^{7} c^{3} + \frac{3}{5} x^{5} c^{2} a + x^{3} c a^{2} + x a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.066568, size = 32, normalized size = 0.91 \begin{align*} a^{3} x + a^{2} c x^{3} + \frac{3 a c^{2} x^{5}}{5} + \frac{c^{3} x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19568, size = 42, normalized size = 1.2 \begin{align*} \frac{1}{7} \, c^{3} x^{7} + \frac{3}{5} \, a c^{2} x^{5} + a^{2} c x^{3} + a^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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