Optimal. Leaf size=17 \[ \frac{b x^5}{5}+\frac{c x^7}{7} \]
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Rubi [A] time = 0.0058893, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {14} \[ \frac{b x^5}{5}+\frac{c x^7}{7} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int x^2 \left (b x^2+c x^4\right ) \, dx &=\int \left (b x^4+c x^6\right ) \, dx\\ &=\frac{b x^5}{5}+\frac{c x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0017171, size = 17, normalized size = 1. \[ \frac{b x^5}{5}+\frac{c x^7}{7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 14, normalized size = 0.8 \begin{align*}{\frac{b{x}^{5}}{5}}+{\frac{c{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.986232, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{7} \, c x^{7} + \frac{1}{5} \, b x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.08648, size = 31, normalized size = 1.82 \begin{align*} \frac{1}{7} x^{7} c + \frac{1}{5} x^{5} b \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.066037, size = 12, normalized size = 0.71 \begin{align*} \frac{b x^{5}}{5} + \frac{c x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.24423, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{7} \, c x^{7} + \frac{1}{5} \, b x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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