Optimal. Leaf size=78 \[ -\frac{1000 (3 x+2)^{11}}{24057}+\frac{370}{729} (3 x+2)^{10}-\frac{14390 (3 x+2)^9}{6561}+\frac{66193 (3 x+2)^8}{17496}-\frac{1439}{729} (3 x+2)^7+\frac{1813 (3 x+2)^6}{4374}-\frac{343 (3 x+2)^5}{10935} \]
[Out]
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Rubi [A] time = 0.106548, 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 \[ -\frac{1000 (3 x+2)^{11}}{24057}+\frac{370}{729} (3 x+2)^{10}-\frac{14390 (3 x+2)^9}{6561}+\frac{66193 (3 x+2)^8}{17496}-\frac{1439}{729} (3 x+2)^7+\frac{1813 (3 x+2)^6}{4374}-\frac{343 (3 x+2)^5}{10935} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{81000 x^{11}}{11} - 24030 x^{10} - 23370 x^{9} + \frac{41619 x^{8}}{8} + 22949 x^{7} + \frac{19607 x^{6}}{2} - \frac{28917 x^{5}}{5} - 5548 x^{4} - 312 x^{3} + 432 x + 2160 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**4*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.00425865, size = 62, normalized size = 0.79 \[ -\frac{81000 x^{11}}{11}-24030 x^{10}-23370 x^9+\frac{41619 x^8}{8}+22949 x^7+\frac{19607 x^6}{2}-\frac{28917 x^5}{5}-5548 x^4-312 x^3+1080 x^2+432 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.001, size = 55, normalized size = 0.7 \[ -{\frac{81000\,{x}^{11}}{11}}-24030\,{x}^{10}-23370\,{x}^{9}+{\frac{41619\,{x}^{8}}{8}}+22949\,{x}^{7}+{\frac{19607\,{x}^{6}}{2}}-{\frac{28917\,{x}^{5}}{5}}-5548\,{x}^{4}-312\,{x}^{3}+1080\,{x}^{2}+432\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34334, size = 73, normalized size = 0.94 \[ -\frac{81000}{11} \, x^{11} - 24030 \, x^{10} - 23370 \, x^{9} + \frac{41619}{8} \, x^{8} + 22949 \, x^{7} + \frac{19607}{2} \, x^{6} - \frac{28917}{5} \, x^{5} - 5548 \, x^{4} - 312 \, x^{3} + 1080 \, x^{2} + 432 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.180595, size = 1, normalized size = 0.01 \[ -\frac{81000}{11} x^{11} - 24030 x^{10} - 23370 x^{9} + \frac{41619}{8} x^{8} + 22949 x^{7} + \frac{19607}{2} x^{6} - \frac{28917}{5} x^{5} - 5548 x^{4} - 312 x^{3} + 1080 x^{2} + 432 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.125126, size = 60, normalized size = 0.77 \[ - \frac{81000 x^{11}}{11} - 24030 x^{10} - 23370 x^{9} + \frac{41619 x^{8}}{8} + 22949 x^{7} + \frac{19607 x^{6}}{2} - \frac{28917 x^{5}}{5} - 5548 x^{4} - 312 x^{3} + 1080 x^{2} + 432 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**4*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.209335, size = 73, normalized size = 0.94 \[ -\frac{81000}{11} \, x^{11} - 24030 \, x^{10} - 23370 \, x^{9} + \frac{41619}{8} \, x^{8} + 22949 \, x^{7} + \frac{19607}{2} \, x^{6} - \frac{28917}{5} \, x^{5} - 5548 \, x^{4} - 312 \, x^{3} + 1080 \, x^{2} + 432 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^3,x, algorithm="giac")
[Out]