Optimal. Leaf size=20 \[ x^3 \left (a+b x^2+c x^4\right )^{p+1} \]
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Rubi [A] time = 0.04, antiderivative size = 20, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.14, size = 20, normalized size = 1.00 \[ x^3 \left (a+b x^2+c x^4\right )^{p+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.06, size = 31, normalized size = 1.55 \[ {\left (c x^{7} + b x^{5} + a x^{3}\right )} {\left (c x^{4} + b x^{2} + a\right )}^{p} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.61, size = 58, normalized size = 2.90 \[ {\left (c x^{4} + b x^{2} + a\right )}^{p} c x^{7} + {\left (c x^{4} + b x^{2} + a\right )}^{p} b x^{5} + {\left (c x^{4} + b x^{2} + a\right )}^{p} a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 21, normalized size = 1.05 \[ x^{3} \left (c \,x^{4}+b \,x^{2}+a \right )^{p +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.03, size = 31, normalized size = 1.55 \[ {\left (c x^{7} + b x^{5} + a x^{3}\right )} {\left (c x^{4} + b x^{2} + a\right )}^{p} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 31, normalized size = 1.55 \[ \left (c\,x^7+b\,x^5+a\,x^3\right )\,{\left (c\,x^4+b\,x^2+a\right )}^p \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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