Optimal. Leaf size=12 \[ a x+\frac{c x^3}{3} \]
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Rubi [A] time = 0.0019781, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a x+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (a+c x^2\right ) \, dx &=a x+\frac{c x^3}{3}\\ \end{align*}
Mathematica [A] time = 0.0000331, size = 12, normalized size = 1. \[ a x+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.046, size = 11, normalized size = 0.9 \begin{align*} ax+{\frac{c{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15432, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{3} \, c x^{3} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.813, size = 23, normalized size = 1.92 \begin{align*} \frac{1}{3} x^{3} c + x a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.070719, size = 8, normalized size = 0.67 \begin{align*} a x + \frac{c x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22671, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{3} \, c x^{3} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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