Optimal. Leaf size=78 \[ -\frac{675}{256} (1-2 x)^{10}+\frac{1275}{32} (1-2 x)^9-\frac{260055 (1-2 x)^8}{1024}+\frac{98209}{112} (1-2 x)^7-\frac{444983}{256} (1-2 x)^6+\frac{302379}{160} (1-2 x)^5-\frac{456533}{512} (1-2 x)^4 \]
[Out]
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Rubi [A] time = 0.101081, 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 \[ -\frac{675}{256} (1-2 x)^{10}+\frac{1275}{32} (1-2 x)^9-\frac{260055 (1-2 x)^8}{1024}+\frac{98209}{112} (1-2 x)^7-\frac{444983}{256} (1-2 x)^6+\frac{302379}{160} (1-2 x)^5-\frac{456533}{512} (1-2 x)^4 \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - 2700 x^{10} - 6900 x^{9} - \frac{14355 x^{8}}{4} + \frac{33013 x^{7}}{7} + \frac{10513 x^{6}}{2} - \frac{1419 x^{5}}{5} - \frac{8693 x^{4}}{4} - 534 x^{3} + 216 x + 756 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**3*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.00416874, size = 59, normalized size = 0.76 \[ -2700 x^{10}-6900 x^9-\frac{14355 x^8}{4}+\frac{33013 x^7}{7}+\frac{10513 x^6}{2}-\frac{1419 x^5}{5}-\frac{8693 x^4}{4}-534 x^3+378 x^2+216 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.001, size = 50, normalized size = 0.6 \[ -2700\,{x}^{10}-6900\,{x}^{9}-{\frac{14355\,{x}^{8}}{4}}+{\frac{33013\,{x}^{7}}{7}}+{\frac{10513\,{x}^{6}}{2}}-{\frac{1419\,{x}^{5}}{5}}-{\frac{8693\,{x}^{4}}{4}}-534\,{x}^{3}+378\,{x}^{2}+216\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^3*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.35066, size = 66, normalized size = 0.85 \[ -2700 \, x^{10} - 6900 \, x^{9} - \frac{14355}{4} \, x^{8} + \frac{33013}{7} \, x^{7} + \frac{10513}{2} \, x^{6} - \frac{1419}{5} \, x^{5} - \frac{8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^3*(2*x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.179252, size = 1, normalized size = 0.01 \[ -2700 x^{10} - 6900 x^{9} - \frac{14355}{4} x^{8} + \frac{33013}{7} x^{7} + \frac{10513}{2} x^{6} - \frac{1419}{5} x^{5} - \frac{8693}{4} x^{4} - 534 x^{3} + 378 x^{2} + 216 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^3*(2*x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.109877, size = 56, normalized size = 0.72 \[ - 2700 x^{10} - 6900 x^{9} - \frac{14355 x^{8}}{4} + \frac{33013 x^{7}}{7} + \frac{10513 x^{6}}{2} - \frac{1419 x^{5}}{5} - \frac{8693 x^{4}}{4} - 534 x^{3} + 378 x^{2} + 216 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**3*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.220359, size = 66, normalized size = 0.85 \[ -2700 \, x^{10} - 6900 \, x^{9} - \frac{14355}{4} \, x^{8} + \frac{33013}{7} \, x^{7} + \frac{10513}{2} \, x^{6} - \frac{1419}{5} \, x^{5} - \frac{8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^3*(2*x - 1)^3,x, algorithm="giac")
[Out]