Optimal. Leaf size=67 \[ \frac{250 (3 x+2)^{14}}{5103}-\frac{3800 (3 x+2)^{13}}{9477}+\frac{8285 (3 x+2)^{12}}{8748}-\frac{4099 (3 x+2)^{11}}{8019}+\frac{763 (3 x+2)^{10}}{7290}-\frac{49 (3 x+2)^9}{6561} \]
[Out]
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Rubi [A] time = 0.120907, 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 \[ \frac{250 (3 x+2)^{14}}{5103}-\frac{3800 (3 x+2)^{13}}{9477}+\frac{8285 (3 x+2)^{12}}{8748}-\frac{4099 (3 x+2)^{11}}{8019}+\frac{763 (3 x+2)^{10}}{7290}-\frac{49 (3 x+2)^9}{6561} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 16.1902, size = 60, normalized size = 0.9 \[ \frac{250 \left (3 x + 2\right )^{14}}{5103} - \frac{3800 \left (3 x + 2\right )^{13}}{9477} + \frac{8285 \left (3 x + 2\right )^{12}}{8748} - \frac{4099 \left (3 x + 2\right )^{11}}{8019} + \frac{763 \left (3 x + 2\right )^{10}}{7290} - \frac{49 \left (3 x + 2\right )^{9}}{6561} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**8*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.00406026, size = 85, normalized size = 1.27 \[ \frac{1640250 x^{14}}{7}+\frac{20120400 x^{13}}{13}+\frac{17759655 x^{12}}{4}+\frac{77509953 x^{11}}{11}+\frac{62652123 x^{10}}{10}+2124195 x^9-1660896 x^8-\frac{17018256 x^7}{7}-\frac{3530000 x^6}{3}-\frac{202208 x^5}{5}+261440 x^4+155136 x^3+44928 x^2+6912 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.002, size = 70, normalized size = 1. \[{\frac{1640250\,{x}^{14}}{7}}+{\frac{20120400\,{x}^{13}}{13}}+{\frac{17759655\,{x}^{12}}{4}}+{\frac{77509953\,{x}^{11}}{11}}+{\frac{62652123\,{x}^{10}}{10}}+2124195\,{x}^{9}-1660896\,{x}^{8}-{\frac{17018256\,{x}^{7}}{7}}-{\frac{3530000\,{x}^{6}}{3}}-{\frac{202208\,{x}^{5}}{5}}+261440\,{x}^{4}+155136\,{x}^{3}+44928\,{x}^{2}+6912\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^8*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.36236, size = 93, normalized size = 1.39 \[ \frac{1640250}{7} \, x^{14} + \frac{20120400}{13} \, x^{13} + \frac{17759655}{4} \, x^{12} + \frac{77509953}{11} \, x^{11} + \frac{62652123}{10} \, x^{10} + 2124195 \, x^{9} - 1660896 \, x^{8} - \frac{17018256}{7} \, x^{7} - \frac{3530000}{3} \, x^{6} - \frac{202208}{5} \, x^{5} + 261440 \, x^{4} + 155136 \, x^{3} + 44928 \, x^{2} + 6912 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^8*(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.183327, size = 1, normalized size = 0.01 \[ \frac{1640250}{7} x^{14} + \frac{20120400}{13} x^{13} + \frac{17759655}{4} x^{12} + \frac{77509953}{11} x^{11} + \frac{62652123}{10} x^{10} + 2124195 x^{9} - 1660896 x^{8} - \frac{17018256}{7} x^{7} - \frac{3530000}{3} x^{6} - \frac{202208}{5} x^{5} + 261440 x^{4} + 155136 x^{3} + 44928 x^{2} + 6912 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^8*(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.135834, size = 82, normalized size = 1.22 \[ \frac{1640250 x^{14}}{7} + \frac{20120400 x^{13}}{13} + \frac{17759655 x^{12}}{4} + \frac{77509953 x^{11}}{11} + \frac{62652123 x^{10}}{10} + 2124195 x^{9} - 1660896 x^{8} - \frac{17018256 x^{7}}{7} - \frac{3530000 x^{6}}{3} - \frac{202208 x^{5}}{5} + 261440 x^{4} + 155136 x^{3} + 44928 x^{2} + 6912 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**8*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.21852, size = 93, normalized size = 1.39 \[ \frac{1640250}{7} \, x^{14} + \frac{20120400}{13} \, x^{13} + \frac{17759655}{4} \, x^{12} + \frac{77509953}{11} \, x^{11} + \frac{62652123}{10} \, x^{10} + 2124195 \, x^{9} - 1660896 \, x^{8} - \frac{17018256}{7} \, x^{7} - \frac{3530000}{3} \, x^{6} - \frac{202208}{5} \, x^{5} + 261440 \, x^{4} + 155136 \, x^{3} + 44928 \, x^{2} + 6912 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^8*(2*x - 1)^2,x, algorithm="giac")
[Out]