Optimal. Leaf size=23 \[ x^2 \left (a+b x+c x^2+d x^3\right )^{p+1} \]
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Rubi [A] time = 0.0590147, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 49, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.02, Rules used = {1588} \[ x^2 \left (a+b x+c x^2+d x^3\right )^{p+1} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int x \left (a+b x+c x^2+d x^3\right )^p \left (2 a+b (3+p) x+c (4+2 p) x^2+d (5+3 p) x^3\right ) \, dx &=x^2 \left (a+b x+c x^2+d x^3\right )^{1+p}\\ \end{align*}
Mathematica [A] time = 0.177702, size = 21, normalized size = 0.91 \[ x^2 (a+x (b+x (c+d x)))^{p+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 24, normalized size = 1. \begin{align*}{x}^{2} \left ( d{x}^{3}+c{x}^{2}+bx+a \right ) ^{1+p} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.20393, size = 53, normalized size = 2.3 \begin{align*}{\left (d x^{5} + c x^{4} + b x^{3} + a x^{2}\right )}{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42424, size = 82, normalized size = 3.57 \begin{align*}{\left (d x^{5} + c x^{4} + b x^{3} + a x^{2}\right )}{\left (d x^{3} + c x^{2} + b x + 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 = 1.36567, size = 120, normalized size = 5.22 \begin{align*}{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} d x^{5} +{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} c x^{4} +{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} b x^{3} +{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} a x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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