Optimal. Leaf size=67 \[ -\frac{20}{729} (3 x+2)^{10}+\frac{2180 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{2916}+\frac{1657}{729} (3 x+2)^7-\frac{1862 (3 x+2)^6}{2187}+\frac{343 (3 x+2)^5}{3645} \]
[Out]
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Rubi [A] time = 0.0984815, 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 \[ -\frac{20}{729} (3 x+2)^{10}+\frac{2180 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{2916}+\frac{1657}{729} (3 x+2)^7-\frac{1862 (3 x+2)^6}{2187}+\frac{343 (3 x+2)^5}{3645} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - 1620 x^{10} - 4260 x^{9} - \frac{9531 x^{8}}{4} + 2823 x^{7} + \frac{10136 x^{6}}{3} - \frac{399 x^{5}}{5} - 1386 x^{4} - \frac{1112 x^{3}}{3} + 144 x + 480 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**4*(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.00392011, size = 57, normalized size = 0.85 \[ -1620 x^{10}-4260 x^9-\frac{9531 x^8}{4}+2823 x^7+\frac{10136 x^6}{3}-\frac{399 x^5}{5}-1386 x^4-\frac{1112 x^3}{3}+240 x^2+144 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.002, size = 50, normalized size = 0.8 \[ -1620\,{x}^{10}-4260\,{x}^{9}-{\frac{9531\,{x}^{8}}{4}}+2823\,{x}^{7}+{\frac{10136\,{x}^{6}}{3}}-{\frac{399\,{x}^{5}}{5}}-1386\,{x}^{4}-{\frac{1112\,{x}^{3}}{3}}+240\,{x}^{2}+144\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^4*(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34118, size = 66, normalized size = 0.99 \[ -1620 \, x^{10} - 4260 \, x^{9} - \frac{9531}{4} \, x^{8} + 2823 \, x^{7} + \frac{10136}{3} \, x^{6} - \frac{399}{5} \, x^{5} - 1386 \, x^{4} - \frac{1112}{3} \, x^{3} + 240 \, x^{2} + 144 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^4*(2*x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.182674, size = 1, normalized size = 0.01 \[ -1620 x^{10} - 4260 x^{9} - \frac{9531}{4} x^{8} + 2823 x^{7} + \frac{10136}{3} x^{6} - \frac{399}{5} x^{5} - 1386 x^{4} - \frac{1112}{3} x^{3} + 240 x^{2} + 144 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^4*(2*x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.104483, size = 54, normalized size = 0.81 \[ - 1620 x^{10} - 4260 x^{9} - \frac{9531 x^{8}}{4} + 2823 x^{7} + \frac{10136 x^{6}}{3} - \frac{399 x^{5}}{5} - 1386 x^{4} - \frac{1112 x^{3}}{3} + 240 x^{2} + 144 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**4*(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.216633, size = 66, normalized size = 0.99 \[ -1620 \, x^{10} - 4260 \, x^{9} - \frac{9531}{4} \, x^{8} + 2823 \, x^{7} + \frac{10136}{3} \, x^{6} - \frac{399}{5} \, x^{5} - 1386 \, x^{4} - \frac{1112}{3} \, x^{3} + 240 \, x^{2} + 144 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^4*(2*x - 1)^3,x, algorithm="giac")
[Out]