Optimal. Leaf size=25 \[ -\frac{16 x^7}{7}+\frac{32 x^5}{5}-\frac{19 x^3}{3}+3 x \]
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Rubi [A] time = 0.0031791, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ -\frac{16 x^7}{7}+\frac{32 x^5}{5}-\frac{19 x^3}{3}+3 x \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (3-19 x^2+32 x^4-16 x^6\right ) \, dx &=3 x-\frac{19 x^3}{3}+\frac{32 x^5}{5}-\frac{16 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0000443, size = 25, normalized size = 1. \[ -\frac{16 x^7}{7}+\frac{32 x^5}{5}-\frac{19 x^3}{3}+3 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 20, normalized size = 0.8 \begin{align*} 3\,x-{\frac{19\,{x}^{3}}{3}}+{\frac{32\,{x}^{5}}{5}}-{\frac{16\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.17189, size = 26, normalized size = 1.04 \begin{align*} -\frac{16}{7} \, x^{7} + \frac{32}{5} \, x^{5} - \frac{19}{3} \, x^{3} + 3 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.43674, size = 53, normalized size = 2.12 \begin{align*} -\frac{16}{7} x^{7} + \frac{32}{5} x^{5} - \frac{19}{3} x^{3} + 3 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.05443, size = 22, normalized size = 0.88 \begin{align*} - \frac{16 x^{7}}{7} + \frac{32 x^{5}}{5} - \frac{19 x^{3}}{3} + 3 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12437, size = 26, normalized size = 1.04 \begin{align*} -\frac{16}{7} \, x^{7} + \frac{32}{5} \, x^{5} - \frac{19}{3} \, x^{3} + 3 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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