Optimal. Leaf size=20 \[ a x+\frac{b x^3}{3}+\frac{c x^5}{5} \]
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Rubi [A] time = 0.0034928, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a x+\frac{b x^3}{3}+\frac{c x^5}{5} \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (a+b x^2+c x^4\right ) \, dx &=a x+\frac{b x^3}{3}+\frac{c x^5}{5}\\ \end{align*}
Mathematica [A] time = 0.0000322, size = 20, normalized size = 1. \[ a x+\frac{b x^3}{3}+\frac{c x^5}{5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 17, normalized size = 0.9 \begin{align*} ax+{\frac{b{x}^{3}}{3}}+{\frac{c{x}^{5}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.970358, size = 22, normalized size = 1.1 \begin{align*} \frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.24892, size = 39, normalized size = 1.95 \begin{align*} \frac{1}{5} x^{5} c + \frac{1}{3} x^{3} b + x a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058773, size = 15, normalized size = 0.75 \begin{align*} a x + \frac{b x^{3}}{3} + \frac{c x^{5}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20711, size = 22, normalized size = 1.1 \begin{align*} \frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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