Optimal. Leaf size=20 \[ x^3 \left (a+b x^2+c x^4\right )^{p+1} \]
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Rubi [A] time = 0.0363838, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 42, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.024, Rules used = {1588} \[ x^3 \left (a+b x^2+c x^4\right )^{p+1} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int x^2 \left (a+b x^2+c x^4\right )^p \left (3 a+b (5+2 p) x^2+c (7+4 p) x^4\right ) \, dx &=x^3 \left (a+b x^2+c x^4\right )^{1+p}\\ \end{align*}
Mathematica [A] time = 0.147311, size = 20, normalized size = 1. \[ x^3 \left (a+b x^2+c x^4\right )^{p+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.014, size = 21, normalized size = 1.1 \begin{align*}{x}^{3} \left ( c{x}^{4}+b{x}^{2}+a \right ) ^{1+p} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.23919, size = 42, normalized size = 2.1 \begin{align*}{\left (c x^{7} + b x^{5} + a x^{3}\right )}{\left (c x^{4} + b x^{2} + a\right )}^{p} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.85655, size = 63, normalized size = 3.15 \begin{align*}{\left (c x^{7} + b x^{5} + a x^{3}\right )}{\left (c x^{4} + b x^{2} + a\right )}^{p} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.1973, size = 78, normalized size = 3.9 \begin{align*}{\left (c x^{4} + b x^{2} + a\right )}^{p} c x^{7} +{\left (c x^{4} + b x^{2} + a\right )}^{p} b x^{5} +{\left (c x^{4} + b x^{2} + a\right )}^{p} a x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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