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 = 0.06, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, 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*}
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Mathematica [A] time = 0.18, 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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fricas [A] time = 0.89, size = 39, normalized size = 1.70 \[ {\left (d x^{5} + c x^{4} + b x^{3} + a x^{2}\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.73, size = 89, normalized size = 3.87 \[ {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} d x^{5} + {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} c x^{4} + {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} b x^{3} + {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 24, normalized size = 1.04 \[ x^{2} \left (d \,x^{3}+c \,x^{2}+b x +a \right )^{p +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 39, normalized size = 1.70 \[ {\left (d x^{5} + c x^{4} + b x^{3} + a x^{2}\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.32, size = 39, normalized size = 1.70 \[ {\left (d\,x^3+c\,x^2+b\,x+a\right )}^p\,\left (d\,x^5+c\,x^4+b\,x^3+a\,x^2\right ) \]
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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