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 = 0.02, antiderivative size = 25, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.37, 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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fricas [A] time = 1.25, size = 40, normalized size = 1.60 \[ {\left (d x^{4} + c x^{3} + b x^{2} + a x\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} x^{m} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 2.09, size = 99, normalized size = 3.96 \[ {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} d x^{4} x^{m} + {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} c x^{3} x^{m} + {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} b x^{2} x^{m} + {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} a x x^{m} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 26, normalized size = 1.04 \[ x^{m +1} \left (d \,x^{3}+c \,x^{2}+b x +a \right )^{p +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.70, size = 44, normalized size = 1.76 \[ {\left (d x^{4} + c x^{3} + b x^{2} + a x\right )} e^{\left (p \log \left (d x^{3} + c x^{2} + b x + a\right ) + m \log \relax (x)\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.66, size = 49, normalized size = 1.96 \[ {\left (d\,x^3+c\,x^2+b\,x+a\right )}^p\,\left (a\,x\,x^m+b\,x^m\,x^2+c\,x^m\,x^3+d\,x^m\,x^4\right ) \]
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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