Optimal. Leaf size=78 \[ -\frac{500 (3 x+2)^{14}}{15309}+\frac{3700 (3 x+2)^{13}}{9477}-\frac{7195 (3 x+2)^{12}}{4374}+\frac{66193 (3 x+2)^{11}}{24057}-\frac{10073 (3 x+2)^{10}}{7290}+\frac{1813 (3 x+2)^9}{6561}-\frac{343 (3 x+2)^8}{17496} \]
[Out]
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Rubi [A] time = 0.131144, antiderivative size = 78, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{500 (3 x+2)^{14}}{15309}+\frac{3700 (3 x+2)^{13}}{9477}-\frac{7195 (3 x+2)^{12}}{4374}+\frac{66193 (3 x+2)^{11}}{24057}-\frac{10073 (3 x+2)^{10}}{7290}+\frac{1813 (3 x+2)^9}{6561}-\frac{343 (3 x+2)^8}{17496} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{1093500 x^{14}}{7} - \frac{10862100 x^{13}}{13} - \frac{3595185 x^{12}}{2} - \frac{19532907 x^{11}}{11} - \frac{2909493 x^{10}}{10} + 1119837 x^{9} + \frac{8511675 x^{8}}{8} + \frac{1241998 x^{7}}{7} - 299014 x^{6} - \frac{1022472 x^{5}}{5} - 20732 x^{4} + 31200 x^{3} + 3456 x + 32832 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**7*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.00484678, size = 85, normalized size = 1.09 \[ -\frac{1093500 x^{14}}{7}-\frac{10862100 x^{13}}{13}-\frac{3595185 x^{12}}{2}-\frac{19532907 x^{11}}{11}-\frac{2909493 x^{10}}{10}+1119837 x^9+\frac{8511675 x^8}{8}+\frac{1241998 x^7}{7}-299014 x^6-\frac{1022472 x^5}{5}-20732 x^4+31200 x^3+16416 x^2+3456 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.003, size = 70, normalized size = 0.9 \[ -{\frac{1093500\,{x}^{14}}{7}}-{\frac{10862100\,{x}^{13}}{13}}-{\frac{3595185\,{x}^{12}}{2}}-{\frac{19532907\,{x}^{11}}{11}}-{\frac{2909493\,{x}^{10}}{10}}+1119837\,{x}^{9}+{\frac{8511675\,{x}^{8}}{8}}+{\frac{1241998\,{x}^{7}}{7}}-299014\,{x}^{6}-{\frac{1022472\,{x}^{5}}{5}}-20732\,{x}^{4}+31200\,{x}^{3}+16416\,{x}^{2}+3456\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^7*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.35016, size = 93, normalized size = 1.19 \[ -\frac{1093500}{7} \, x^{14} - \frac{10862100}{13} \, x^{13} - \frac{3595185}{2} \, x^{12} - \frac{19532907}{11} \, x^{11} - \frac{2909493}{10} \, x^{10} + 1119837 \, x^{9} + \frac{8511675}{8} \, x^{8} + \frac{1241998}{7} \, x^{7} - 299014 \, x^{6} - \frac{1022472}{5} \, x^{5} - 20732 \, x^{4} + 31200 \, x^{3} + 16416 \, x^{2} + 3456 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^7*(2*x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.178961, size = 1, normalized size = 0.01 \[ -\frac{1093500}{7} x^{14} - \frac{10862100}{13} x^{13} - \frac{3595185}{2} x^{12} - \frac{19532907}{11} x^{11} - \frac{2909493}{10} x^{10} + 1119837 x^{9} + \frac{8511675}{8} x^{8} + \frac{1241998}{7} x^{7} - 299014 x^{6} - \frac{1022472}{5} x^{5} - 20732 x^{4} + 31200 x^{3} + 16416 x^{2} + 3456 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^7*(2*x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.131499, size = 82, normalized size = 1.05 \[ - \frac{1093500 x^{14}}{7} - \frac{10862100 x^{13}}{13} - \frac{3595185 x^{12}}{2} - \frac{19532907 x^{11}}{11} - \frac{2909493 x^{10}}{10} + 1119837 x^{9} + \frac{8511675 x^{8}}{8} + \frac{1241998 x^{7}}{7} - 299014 x^{6} - \frac{1022472 x^{5}}{5} - 20732 x^{4} + 31200 x^{3} + 16416 x^{2} + 3456 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**7*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.210019, size = 93, normalized size = 1.19 \[ -\frac{1093500}{7} \, x^{14} - \frac{10862100}{13} \, x^{13} - \frac{3595185}{2} \, x^{12} - \frac{19532907}{11} \, x^{11} - \frac{2909493}{10} \, x^{10} + 1119837 \, x^{9} + \frac{8511675}{8} \, x^{8} + \frac{1241998}{7} \, x^{7} - 299014 \, x^{6} - \frac{1022472}{5} \, x^{5} - 20732 \, x^{4} + 31200 \, x^{3} + 16416 \, x^{2} + 3456 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^7*(2*x - 1)^3,x, algorithm="giac")
[Out]