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 = 0.04, antiderivative size = 21, normalized size of antiderivative = 1.00, 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} \begin {gather*} x \left (a+b x+c x^2+d x^3\right )^{p+1} \end {gather*}
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*}
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Mathematica [A] time = 0.12, size = 19, normalized size = 0.90 \begin {gather*} x (a+x (b+x (c+d x)))^{p+1} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.56, size = 0, normalized size = 0.00 \begin {gather*} \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 \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.26, size = 37, normalized size = 1.76 \begin {gather*} {\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.08, size = 87, normalized size = 4.14 \begin {gather*} {\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 22, normalized size = 1.05 \begin {gather*} x \left (d \,x^{3}+c \,x^{2}+b x +a \right )^{p +1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 37, normalized size = 1.76 \begin {gather*} {\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.27, size = 37, normalized size = 1.76 \begin {gather*} {\left (d\,x^3+c\,x^2+b\,x+a\right )}^p\,\left (d\,x^4+c\,x^3+b\,x^2+a\,x\right ) \end {gather*}
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 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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