Optimal. Leaf size=67 \[ \frac{50}{729} (3 x+2)^{10}-\frac{3800 (3 x+2)^9}{6561}+\frac{8285 (3 x+2)^8}{5832}-\frac{4099 (3 x+2)^7}{5103}+\frac{763 (3 x+2)^6}{4374}-\frac{49 (3 x+2)^5}{3645} \]
[Out]
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Rubi [A] time = 0.098772, 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 \[ \frac{50}{729} (3 x+2)^{10}-\frac{3800 (3 x+2)^9}{6561}+\frac{8285 (3 x+2)^8}{5832}-\frac{4099 (3 x+2)^7}{5103}+\frac{763 (3 x+2)^6}{4374}-\frac{49 (3 x+2)^5}{3645} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2*(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. \[ 4050 x^{10} + 15600 x^{9} + \frac{175365 x^{8}}{8} + \frac{66873 x^{7}}{7} - \frac{46885 x^{6}}{6} - \frac{52853 x^{5}}{5} - 2992 x^{4} + 1704 x^{3} + 432 x + 3024 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**4*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.00430665, size = 57, normalized size = 0.85 \[ 4050 x^{10}+15600 x^9+\frac{175365 x^8}{8}+\frac{66873 x^7}{7}-\frac{46885 x^6}{6}-\frac{52853 x^5}{5}-2992 x^4+1704 x^3+1512 x^2+432 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.001, size = 50, normalized size = 0.8 \[ 4050\,{x}^{10}+15600\,{x}^{9}+{\frac{175365\,{x}^{8}}{8}}+{\frac{66873\,{x}^{7}}{7}}-{\frac{46885\,{x}^{6}}{6}}-{\frac{52853\,{x}^{5}}{5}}-2992\,{x}^{4}+1704\,{x}^{3}+1512\,{x}^{2}+432\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34397, size = 66, normalized size = 0.99 \[ 4050 \, x^{10} + 15600 \, x^{9} + \frac{175365}{8} \, x^{8} + \frac{66873}{7} \, x^{7} - \frac{46885}{6} \, x^{6} - \frac{52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.179436, size = 1, normalized size = 0.01 \[ 4050 x^{10} + 15600 x^{9} + \frac{175365}{8} x^{8} + \frac{66873}{7} x^{7} - \frac{46885}{6} x^{6} - \frac{52853}{5} x^{5} - 2992 x^{4} + 1704 x^{3} + 1512 x^{2} + 432 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.111172, size = 54, normalized size = 0.81 \[ 4050 x^{10} + 15600 x^{9} + \frac{175365 x^{8}}{8} + \frac{66873 x^{7}}{7} - \frac{46885 x^{6}}{6} - \frac{52853 x^{5}}{5} - 2992 x^{4} + 1704 x^{3} + 1512 x^{2} + 432 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**4*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.230111, size = 66, normalized size = 0.99 \[ 4050 \, x^{10} + 15600 \, x^{9} + \frac{175365}{8} \, x^{8} + \frac{66873}{7} \, x^{7} - \frac{46885}{6} \, x^{6} - \frac{52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^2,x, algorithm="giac")
[Out]