Optimal. Leaf size=113 \[ a^4 c x+\frac{1}{2} a^4 d x^2+a^3 b c x^4+\frac{4}{5} a^3 b d x^5+\frac{6}{7} a^2 b^2 c x^7+\frac{3}{4} a^2 b^2 d x^8+\frac{2}{5} a b^3 c x^{10}+\frac{4}{11} a b^3 d x^{11}+\frac{1}{13} b^4 c x^{13}+\frac{1}{14} b^4 d x^{14} \]
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Rubi [A] time = 0.174886, antiderivative size = 113, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.033 \[ a^4 c x+\frac{1}{2} a^4 d x^2+a^3 b c x^4+\frac{4}{5} a^3 b d x^5+\frac{6}{7} a^2 b^2 c x^7+\frac{3}{4} a^2 b^2 d x^8+\frac{2}{5} a b^3 c x^{10}+\frac{4}{11} a b^3 d x^{11}+\frac{1}{13} b^4 c x^{13}+\frac{1}{14} b^4 d x^{14} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^3*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{4} d \int x\, dx + a^{4} \int c\, dx + a^{3} b c x^{4} + \frac{4 a^{3} b d x^{5}}{5} + \frac{6 a^{2} b^{2} c x^{7}}{7} + \frac{3 a^{2} b^{2} d x^{8}}{4} + \frac{2 a b^{3} c x^{10}}{5} + \frac{4 a b^{3} d x^{11}}{11} + \frac{b^{4} c x^{13}}{13} + \frac{b^{4} d x^{14}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3*(b*d*x**4+b*c*x**3+a*d*x+a*c),x)
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Mathematica [A] time = 0.00787382, size = 113, normalized size = 1. \[ a^4 c x+\frac{1}{2} a^4 d x^2+a^3 b c x^4+\frac{4}{5} a^3 b d x^5+\frac{6}{7} a^2 b^2 c x^7+\frac{3}{4} a^2 b^2 d x^8+\frac{2}{5} a b^3 c x^{10}+\frac{4}{11} a b^3 d x^{11}+\frac{1}{13} b^4 c x^{13}+\frac{1}{14} b^4 d x^{14} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^3*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x]
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Maple [A] time = 0.003, size = 98, normalized size = 0.9 \[{a}^{4}cx+{\frac{{a}^{4}d{x}^{2}}{2}}+{a}^{3}bc{x}^{4}+{\frac{4\,{a}^{3}bd{x}^{5}}{5}}+{\frac{6\,{a}^{2}{b}^{2}c{x}^{7}}{7}}+{\frac{3\,{a}^{2}{b}^{2}d{x}^{8}}{4}}+{\frac{2\,a{b}^{3}c{x}^{10}}{5}}+{\frac{4\,a{b}^{3}d{x}^{11}}{11}}+{\frac{{b}^{4}c{x}^{13}}{13}}+{\frac{{b}^{4}d{x}^{14}}{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3*(b*d*x^4+b*c*x^3+a*d*x+a*c),x)
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Maxima [A] time = 1.42368, size = 131, normalized size = 1.16 \[ \frac{1}{14} \, b^{4} d x^{14} + \frac{1}{13} \, b^{4} c x^{13} + \frac{4}{11} \, a b^{3} d x^{11} + \frac{2}{5} \, a b^{3} c x^{10} + \frac{3}{4} \, a^{2} b^{2} d x^{8} + \frac{6}{7} \, a^{2} b^{2} c x^{7} + \frac{4}{5} \, a^{3} b d x^{5} + a^{3} b c x^{4} + \frac{1}{2} \, a^{4} d x^{2} + a^{4} c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)*(b*x^3 + a)^3,x, algorithm="maxima")
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Fricas [A] time = 0.206957, size = 1, normalized size = 0.01 \[ \frac{1}{14} x^{14} d b^{4} + \frac{1}{13} x^{13} c b^{4} + \frac{4}{11} x^{11} d b^{3} a + \frac{2}{5} x^{10} c b^{3} a + \frac{3}{4} x^{8} d b^{2} a^{2} + \frac{6}{7} x^{7} c b^{2} a^{2} + \frac{4}{5} x^{5} d b a^{3} + x^{4} c b a^{3} + \frac{1}{2} x^{2} d a^{4} + x c a^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)*(b*x^3 + a)^3,x, algorithm="fricas")
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Sympy [A] time = 0.082327, size = 117, normalized size = 1.04 \[ a^{4} c x + \frac{a^{4} d x^{2}}{2} + a^{3} b c x^{4} + \frac{4 a^{3} b d x^{5}}{5} + \frac{6 a^{2} b^{2} c x^{7}}{7} + \frac{3 a^{2} b^{2} d x^{8}}{4} + \frac{2 a b^{3} c x^{10}}{5} + \frac{4 a b^{3} d x^{11}}{11} + \frac{b^{4} c x^{13}}{13} + \frac{b^{4} d x^{14}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3*(b*d*x**4+b*c*x**3+a*d*x+a*c),x)
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GIAC/XCAS [A] time = 0.214945, size = 131, normalized size = 1.16 \[ \frac{1}{14} \, b^{4} d x^{14} + \frac{1}{13} \, b^{4} c x^{13} + \frac{4}{11} \, a b^{3} d x^{11} + \frac{2}{5} \, a b^{3} c x^{10} + \frac{3}{4} \, a^{2} b^{2} d x^{8} + \frac{6}{7} \, a^{2} b^{2} c x^{7} + \frac{4}{5} \, a^{3} b d x^{5} + a^{3} b c x^{4} + \frac{1}{2} \, a^{4} d x^{2} + a^{4} c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)*(b*x^3 + a)^3,x, algorithm="giac")
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