Optimal. Leaf size=67 \[ \frac{500 (3 x+2)^{13}}{9477}-\frac{950 (3 x+2)^{12}}{2187}+\frac{8285 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{7290}+\frac{763 (3 x+2)^9}{6561}-\frac{49 (3 x+2)^8}{5832} \]
[Out]
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Rubi [A] time = 0.109716, antiderivative size = 67, 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 \[ \frac{500 (3 x+2)^{13}}{9477}-\frac{950 (3 x+2)^{12}}{2187}+\frac{8285 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{7290}+\frac{763 (3 x+2)^9}{6561}-\frac{49 (3 x+2)^8}{5832} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 15.3594, size = 60, normalized size = 0.9 \[ \frac{500 \left (3 x + 2\right )^{13}}{9477} - \frac{950 \left (3 x + 2\right )^{12}}{2187} + \frac{8285 \left (3 x + 2\right )^{11}}{8019} - \frac{4099 \left (3 x + 2\right )^{10}}{7290} + \frac{763 \left (3 x + 2\right )^{9}}{6561} - \frac{49 \left (3 x + 2\right )^{8}}{5832} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**7*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.00392139, size = 76, normalized size = 1.13 \[ \frac{1093500 x^{13}}{13}+498150 x^{12}+\frac{13774455 x^{11}}{11}+\frac{16653681 x^{10}}{10}+1086843 x^9-\frac{148473 x^8}{8}-618582 x^7-\frac{1393018 x^6}{3}-\frac{495976 x^5}{5}+65812 x^4+57696 x^3+19872 x^2+3456 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.003, size = 65, normalized size = 1. \[{\frac{1093500\,{x}^{13}}{13}}+498150\,{x}^{12}+{\frac{13774455\,{x}^{11}}{11}}+{\frac{16653681\,{x}^{10}}{10}}+1086843\,{x}^{9}-{\frac{148473\,{x}^{8}}{8}}-618582\,{x}^{7}-{\frac{1393018\,{x}^{6}}{3}}-{\frac{495976\,{x}^{5}}{5}}+65812\,{x}^{4}+57696\,{x}^{3}+19872\,{x}^{2}+3456\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.33277, size = 86, normalized size = 1.28 \[ \frac{1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac{13774455}{11} \, x^{11} + \frac{16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac{148473}{8} \, x^{8} - 618582 \, x^{7} - \frac{1393018}{3} \, x^{6} - \frac{495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^7*(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.181853, size = 1, normalized size = 0.01 \[ \frac{1093500}{13} x^{13} + 498150 x^{12} + \frac{13774455}{11} x^{11} + \frac{16653681}{10} x^{10} + 1086843 x^{9} - \frac{148473}{8} x^{8} - 618582 x^{7} - \frac{1393018}{3} x^{6} - \frac{495976}{5} x^{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^7*(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.128481, size = 73, normalized size = 1.09 \[ \frac{1093500 x^{13}}{13} + 498150 x^{12} + \frac{13774455 x^{11}}{11} + \frac{16653681 x^{10}}{10} + 1086843 x^{9} - \frac{148473 x^{8}}{8} - 618582 x^{7} - \frac{1393018 x^{6}}{3} - \frac{495976 x^{5}}{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**7*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.221915, size = 86, normalized size = 1.28 \[ \frac{1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac{13774455}{11} \, x^{11} + \frac{16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac{148473}{8} \, x^{8} - 618582 \, x^{7} - \frac{1393018}{3} \, x^{6} - \frac{495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^7*(2*x - 1)^2,x, algorithm="giac")
[Out]