Optimal. Leaf size=87 \[ \frac {1}{4} a^5 c^4 x^4-\frac {3}{5} a^4 b c^4 x^5+\frac {1}{3} a^3 b^2 c^4 x^6+\frac {2}{7} a^2 b^3 c^4 x^7-\frac {3}{8} a b^4 c^4 x^8+\frac {1}{9} b^5 c^4 x^9 \]
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Rubi [A] time = 0.04, antiderivative size = 87, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {75} \[ \frac {2}{7} a^2 b^3 c^4 x^7+\frac {1}{3} a^3 b^2 c^4 x^6-\frac {3}{5} a^4 b c^4 x^5+\frac {1}{4} a^5 c^4 x^4-\frac {3}{8} a b^4 c^4 x^8+\frac {1}{9} b^5 c^4 x^9 \]
Antiderivative was successfully verified.
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Rule 75
Rubi steps
\begin {align*} \int x^3 (a+b x) (a c-b c x)^4 \, dx &=\int \left (a^5 c^4 x^3-3 a^4 b c^4 x^4+2 a^3 b^2 c^4 x^5+2 a^2 b^3 c^4 x^6-3 a b^4 c^4 x^7+b^5 c^4 x^8\right ) \, dx\\ &=\frac {1}{4} a^5 c^4 x^4-\frac {3}{5} a^4 b c^4 x^5+\frac {1}{3} a^3 b^2 c^4 x^6+\frac {2}{7} a^2 b^3 c^4 x^7-\frac {3}{8} a b^4 c^4 x^8+\frac {1}{9} b^5 c^4 x^9\\ \end {align*}
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Mathematica [A] time = 0.00, size = 87, normalized size = 1.00 \[ \frac {1}{4} a^5 c^4 x^4-\frac {3}{5} a^4 b c^4 x^5+\frac {1}{3} a^3 b^2 c^4 x^6+\frac {2}{7} a^2 b^3 c^4 x^7-\frac {3}{8} a b^4 c^4 x^8+\frac {1}{9} b^5 c^4 x^9 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 75, normalized size = 0.86 \[ \frac {1}{9} x^{9} c^{4} b^{5} - \frac {3}{8} x^{8} c^{4} b^{4} a + \frac {2}{7} x^{7} c^{4} b^{3} a^{2} + \frac {1}{3} x^{6} c^{4} b^{2} a^{3} - \frac {3}{5} x^{5} c^{4} b a^{4} + \frac {1}{4} x^{4} c^{4} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.83, size = 75, normalized size = 0.86 \[ \frac {1}{9} \, b^{5} c^{4} x^{9} - \frac {3}{8} \, a b^{4} c^{4} x^{8} + \frac {2}{7} \, a^{2} b^{3} c^{4} x^{7} + \frac {1}{3} \, a^{3} b^{2} c^{4} x^{6} - \frac {3}{5} \, a^{4} b c^{4} x^{5} + \frac {1}{4} \, a^{5} c^{4} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 76, normalized size = 0.87 \[ \frac {1}{9} b^{5} c^{4} x^{9}-\frac {3}{8} a \,b^{4} c^{4} x^{8}+\frac {2}{7} a^{2} b^{3} c^{4} x^{7}+\frac {1}{3} a^{3} b^{2} c^{4} x^{6}-\frac {3}{5} a^{4} b \,c^{4} x^{5}+\frac {1}{4} a^{5} c^{4} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.17, size = 75, normalized size = 0.86 \[ \frac {1}{9} \, b^{5} c^{4} x^{9} - \frac {3}{8} \, a b^{4} c^{4} x^{8} + \frac {2}{7} \, a^{2} b^{3} c^{4} x^{7} + \frac {1}{3} \, a^{3} b^{2} c^{4} x^{6} - \frac {3}{5} \, a^{4} b c^{4} x^{5} + \frac {1}{4} \, a^{5} c^{4} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 75, normalized size = 0.86 \[ \frac {a^5\,c^4\,x^4}{4}-\frac {3\,a^4\,b\,c^4\,x^5}{5}+\frac {a^3\,b^2\,c^4\,x^6}{3}+\frac {2\,a^2\,b^3\,c^4\,x^7}{7}-\frac {3\,a\,b^4\,c^4\,x^8}{8}+\frac {b^5\,c^4\,x^9}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 85, normalized size = 0.98 \[ \frac {a^{5} c^{4} x^{4}}{4} - \frac {3 a^{4} b c^{4} x^{5}}{5} + \frac {a^{3} b^{2} c^{4} x^{6}}{3} + \frac {2 a^{2} b^{3} c^{4} x^{7}}{7} - \frac {3 a b^{4} c^{4} x^{8}}{8} + \frac {b^{5} c^{4} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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