Optimal. Leaf size=67 \[ -\frac{50 (3 x+2)^{12}}{2187}+\frac{2180 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{3645}+\frac{11599 (3 x+2)^9}{6561}-\frac{931 (3 x+2)^8}{1458}+\frac{49}{729} (3 x+2)^7 \]
[Out]
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Rubi [A] time = 0.111393, 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 \[ -\frac{50 (3 x+2)^{12}}{2187}+\frac{2180 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{3645}+\frac{11599 (3 x+2)^9}{6561}-\frac{931 (3 x+2)^8}{1458}+\frac{49}{729} (3 x+2)^7 \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - 12150 x^{12} - \frac{539460 x^{11}}{11} - \frac{348219 x^{10}}{5} - 22695 x^{9} + \frac{85833 x^{8}}{2} + 45531 x^{7} + \frac{13202 x^{6}}{3} - \frac{78132 x^{5}}{5} - 7800 x^{4} + \frac{2608 x^{3}}{3} + 576 x + 3648 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**6*(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.00379852, size = 71, normalized size = 1.06 \[ -12150 x^{12}-\frac{539460 x^{11}}{11}-\frac{348219 x^{10}}{5}-22695 x^9+\frac{85833 x^8}{2}+45531 x^7+\frac{13202 x^6}{3}-\frac{78132 x^5}{5}-7800 x^4+\frac{2608 x^3}{3}+1824 x^2+576 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.001, size = 60, normalized size = 0.9 \[ -12150\,{x}^{12}-{\frac{539460\,{x}^{11}}{11}}-{\frac{348219\,{x}^{10}}{5}}-22695\,{x}^{9}+{\frac{85833\,{x}^{8}}{2}}+45531\,{x}^{7}+{\frac{13202\,{x}^{6}}{3}}-{\frac{78132\,{x}^{5}}{5}}-7800\,{x}^{4}+{\frac{2608\,{x}^{3}}{3}}+1824\,{x}^{2}+576\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^6*(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34996, size = 80, normalized size = 1.19 \[ -12150 \, x^{12} - \frac{539460}{11} \, x^{11} - \frac{348219}{5} \, x^{10} - 22695 \, x^{9} + \frac{85833}{2} \, x^{8} + 45531 \, x^{7} + \frac{13202}{3} \, x^{6} - \frac{78132}{5} \, x^{5} - 7800 \, x^{4} + \frac{2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^6*(2*x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.184758, size = 1, normalized size = 0.01 \[ -12150 x^{12} - \frac{539460}{11} x^{11} - \frac{348219}{5} x^{10} - 22695 x^{9} + \frac{85833}{2} x^{8} + 45531 x^{7} + \frac{13202}{3} x^{6} - \frac{78132}{5} x^{5} - 7800 x^{4} + \frac{2608}{3} x^{3} + 1824 x^{2} + 576 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^6*(2*x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.11623, size = 68, normalized size = 1.01 \[ - 12150 x^{12} - \frac{539460 x^{11}}{11} - \frac{348219 x^{10}}{5} - 22695 x^{9} + \frac{85833 x^{8}}{2} + 45531 x^{7} + \frac{13202 x^{6}}{3} - \frac{78132 x^{5}}{5} - 7800 x^{4} + \frac{2608 x^{3}}{3} + 1824 x^{2} + 576 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**6*(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.212751, size = 80, normalized size = 1.19 \[ -12150 \, x^{12} - \frac{539460}{11} \, x^{11} - \frac{348219}{5} \, x^{10} - 22695 \, x^{9} + \frac{85833}{2} \, x^{8} + 45531 \, x^{7} + \frac{13202}{3} \, x^{6} - \frac{78132}{5} \, x^{5} - 7800 \, x^{4} + \frac{2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^6*(2*x - 1)^3,x, algorithm="giac")
[Out]