Optimal. Leaf size=73 \[ \frac {1}{4} a c x^4+\frac {1}{5} a d x^5+\frac {1}{6} a e x^6+\frac {1}{7} a f x^7+\frac {1}{8} b c x^8+\frac {1}{9} b d x^9+\frac {1}{10} b e x^{10}+\frac {1}{11} b f x^{11} \]
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Rubi [A]
time = 0.04, antiderivative size = 73, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {1834}
\begin {gather*} \frac {1}{4} a c x^4+\frac {1}{5} a d x^5+\frac {1}{6} a e x^6+\frac {1}{7} a f x^7+\frac {1}{8} b c x^8+\frac {1}{9} b d x^9+\frac {1}{10} b e x^{10}+\frac {1}{11} b f x^{11} \end {gather*}
Antiderivative was successfully verified.
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Rule 1834
Rubi steps
\begin {align*} \int x^3 \left (c+d x+e x^2+f x^3\right ) \left (a+b x^4\right ) \, dx &=\int \left (a c x^3+a d x^4+a e x^5+a f x^6+b c x^7+b d x^8+b e x^9+b f x^{10}\right ) \, dx\\ &=\frac {1}{4} a c x^4+\frac {1}{5} a d x^5+\frac {1}{6} a e x^6+\frac {1}{7} a f x^7+\frac {1}{8} b c x^8+\frac {1}{9} b d x^9+\frac {1}{10} b e x^{10}+\frac {1}{11} b f x^{11}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 73, normalized size = 1.00 \begin {gather*} \frac {1}{4} a c x^4+\frac {1}{5} a d x^5+\frac {1}{6} a e x^6+\frac {1}{7} a f x^7+\frac {1}{8} b c x^8+\frac {1}{9} b d x^9+\frac {1}{10} b e x^{10}+\frac {1}{11} b f x^{11} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 58, normalized size = 0.79
method | result | size |
gosper | \(\frac {1}{4} a c \,x^{4}+\frac {1}{5} a d \,x^{5}+\frac {1}{6} a e \,x^{6}+\frac {1}{7} a f \,x^{7}+\frac {1}{8} b c \,x^{8}+\frac {1}{9} b d \,x^{9}+\frac {1}{10} b e \,x^{10}+\frac {1}{11} b f \,x^{11}\) | \(58\) |
default | \(\frac {1}{4} a c \,x^{4}+\frac {1}{5} a d \,x^{5}+\frac {1}{6} a e \,x^{6}+\frac {1}{7} a f \,x^{7}+\frac {1}{8} b c \,x^{8}+\frac {1}{9} b d \,x^{9}+\frac {1}{10} b e \,x^{10}+\frac {1}{11} b f \,x^{11}\) | \(58\) |
norman | \(\frac {1}{4} a c \,x^{4}+\frac {1}{5} a d \,x^{5}+\frac {1}{6} a e \,x^{6}+\frac {1}{7} a f \,x^{7}+\frac {1}{8} b c \,x^{8}+\frac {1}{9} b d \,x^{9}+\frac {1}{10} b e \,x^{10}+\frac {1}{11} b f \,x^{11}\) | \(58\) |
risch | \(\frac {1}{4} a c \,x^{4}+\frac {1}{5} a d \,x^{5}+\frac {1}{6} a e \,x^{6}+\frac {1}{7} a f \,x^{7}+\frac {1}{8} b c \,x^{8}+\frac {1}{9} b d \,x^{9}+\frac {1}{10} b e \,x^{10}+\frac {1}{11} b f \,x^{11}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 59, normalized size = 0.81 \begin {gather*} \frac {1}{11} \, b f x^{11} + \frac {1}{10} \, b x^{10} e + \frac {1}{9} \, b d x^{9} + \frac {1}{8} \, b c x^{8} + \frac {1}{7} \, a f x^{7} + \frac {1}{6} \, a x^{6} e + \frac {1}{5} \, a d x^{5} + \frac {1}{4} \, a c x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 57, normalized size = 0.78 \begin {gather*} \frac {1}{11} \, b f x^{11} + \frac {1}{10} \, b e x^{10} + \frac {1}{9} \, b d x^{9} + \frac {1}{8} \, b c x^{8} + \frac {1}{7} \, a f x^{7} + \frac {1}{6} \, a e x^{6} + \frac {1}{5} \, a d x^{5} + \frac {1}{4} \, a c x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 66, normalized size = 0.90 \begin {gather*} \frac {a c x^{4}}{4} + \frac {a d x^{5}}{5} + \frac {a e x^{6}}{6} + \frac {a f x^{7}}{7} + \frac {b c x^{8}}{8} + \frac {b d x^{9}}{9} + \frac {b e x^{10}}{10} + \frac {b f x^{11}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 59, normalized size = 0.81 \begin {gather*} \frac {1}{11} \, b f x^{11} + \frac {1}{10} \, b x^{10} e + \frac {1}{9} \, b d x^{9} + \frac {1}{8} \, b c x^{8} + \frac {1}{7} \, a f x^{7} + \frac {1}{6} \, a x^{6} e + \frac {1}{5} \, a d x^{5} + \frac {1}{4} \, a c x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 57, normalized size = 0.78 \begin {gather*} \frac {b\,f\,x^{11}}{11}+\frac {b\,e\,x^{10}}{10}+\frac {b\,d\,x^9}{9}+\frac {b\,c\,x^8}{8}+\frac {a\,f\,x^7}{7}+\frac {a\,e\,x^6}{6}+\frac {a\,d\,x^5}{5}+\frac {a\,c\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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