Optimal. Leaf size=25 \[ x^{m+1} \left (a+b x+c x^2+d x^3\right )^{p+1} \]
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Rubi [A] time = 0.0247382, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 56, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.018, Rules used = {1590} \[ x^{m+1} \left (a+b x+c x^2+d x^3\right )^{p+1} \]
Antiderivative was successfully verified.
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Rule 1590
Rubi steps
\begin{align*} \int x^m \left (a+b x+c x^2+d x^3\right )^p (a (1+m)+x (b (2+m+p)+x (c (3+m+2 p)+d (4+m+3 p) x))) \, dx &=x^{1+m} \left (a+b x+c x^2+d x^3\right )^{1+p}\\ \end{align*}
Mathematica [A] time = 0.336487, size = 23, normalized size = 0.92 \[ x^{m+1} (a+x (b+x (c+d x)))^{p+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 26, normalized size = 1. \begin{align*}{x}^{1+m} \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 = 1.3811, size = 59, normalized size = 2.36 \begin{align*}{\left (d x^{4} + c x^{3} + b x^{2} + a x\right )} e^{\left (p \log \left (d x^{3} + c x^{2} + b x + a\right ) + m \log \left (x\right )\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 3.31732, size = 85, normalized size = 3.4 \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} x^{m} \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 = 1.61687, size = 134, normalized size = 5.36 \begin{align*}{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} d x^{4} x^{m} +{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} c x^{3} x^{m} +{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} b x^{2} x^{m} +{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} a x x^{m} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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