Optimal. Leaf size=30 \[ \frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]
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Rubi [A] time = 0.0131603, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {1593, 270} \[ \frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]
Antiderivative was successfully verified.
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Rule 1593
Rule 270
Rubi steps
\begin{align*} \int \left (b x^2+c x^4\right )^2 \, dx &=\int x^4 \left (b+c x^2\right )^2 \, dx\\ &=\int \left (b^2 x^4+2 b c x^6+c^2 x^8\right ) \, dx\\ &=\frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9}\\ \end{align*}
Mathematica [A] time = 0.0012875, size = 30, normalized size = 1. \[ \frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 25, normalized size = 0.8 \begin{align*}{\frac{{b}^{2}{x}^{5}}{5}}+{\frac{2\,bc{x}^{7}}{7}}+{\frac{{c}^{2}{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.970388, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.06599, size = 55, normalized size = 1.83 \begin{align*} \frac{1}{9} x^{9} c^{2} + \frac{2}{7} x^{7} c b + \frac{1}{5} x^{5} b^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.065676, size = 26, normalized size = 0.87 \begin{align*} \frac{b^{2} x^{5}}{5} + \frac{2 b c x^{7}}{7} + \frac{c^{2} x^{9}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.27854, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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