Optimal. Leaf size=25 \[ x^{1+m} \left (a+b x+c x^2+d x^3\right )^{1+p} \]
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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 = {1604}
\begin {gather*} x^{m+1} \left (a+b x+c x^2+d x^3\right )^{p+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 1604
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 = 1.22, size = 23, normalized size = 0.92 \begin {gather*} x^{1+m} (a+x (b+x (c+d x)))^{1+p} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 26, normalized size = 1.04
method | result | size |
gosper | \(x^{1+m} \left (d \,x^{3}+c \,x^{2}+b x +a \right )^{1+p}\) | \(26\) |
risch | \(\left (d \,x^{3}+c \,x^{2}+b x +a \right )^{p} x^{m} x \left (d \,x^{3}+c \,x^{2}+b x +a \right )\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 44, normalized size = 1.76 \begin {gather*} {\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.56, size = 40, normalized size = 1.60 \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} x^{m} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 99 vs.
\(2 (25) = 50\).
time = 6.68, size = 99, normalized size = 3.96 \begin {gather*} {\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 {gather*}
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 \begin {gather*} {\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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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