Optimal. Leaf size=21 \[ x \left (a+b x+c x^2+d x^3\right )^{p+1} \]
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Rubi [A] time = 0.0436484, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 46, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.022, Rules used = {1588} \[ x \left (a+b x+c x^2+d x^3\right )^{p+1} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \left (a+b x+c x^2+d x^3\right )^p \left (a+b (2+p) x+c (3+2 p) x^2+d (4+3 p) x^3\right ) \, dx &=x \left (a+b x+c x^2+d x^3\right )^{1+p}\\ \end{align*}
Mathematica [A] time = 0.119521, size = 19, normalized size = 0.9 \[ x (a+x (b+x (c+d x)))^{p+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 22, normalized size = 1.1 \begin{align*} x \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 = 1.21642, size = 50, normalized size = 2.38 \begin{align*}{\left (d x^{4} + c x^{3} + b x^{2} + a x\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 = 1.46482, size = 80, normalized size = 3.81 \begin{align*}{\left (d x^{4} + c x^{3} + b x^{2} + a x\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 = 1.28569, size = 117, normalized size = 5.57 \begin{align*}{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} d x^{4} +{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} c x^{3} +{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} b x^{2} +{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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