3.1340 \(\int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx\)

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]

(49*(2 + 3*x)^7)/729 - (931*(2 + 3*x)^8)/1458 + (11599*(2 + 3*x)^9)/6561 - (4099
*(2 + 3*x)^10)/3645 + (2180*(2 + 3*x)^11)/8019 - (50*(2 + 3*x)^12)/2187

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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]

(49*(2 + 3*x)^7)/729 - (931*(2 + 3*x)^8)/1458 + (11599*(2 + 3*x)^9)/6561 - (4099
*(2 + 3*x)^10)/3645 + (2180*(2 + 3*x)^11)/8019 - (50*(2 + 3*x)^12)/2187

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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]

-12150*x**12 - 539460*x**11/11 - 348219*x**10/5 - 22695*x**9 + 85833*x**8/2 + 45
531*x**7 + 13202*x**6/3 - 78132*x**5/5 - 7800*x**4 + 2608*x**3/3 + 576*x + 3648*
Integral(x, x)

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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]

576*x + 1824*x^2 + (2608*x^3)/3 - 7800*x^4 - (78132*x^5)/5 + (13202*x^6)/3 + 455
31*x^7 + (85833*x^8)/2 - 22695*x^9 - (348219*x^10)/5 - (539460*x^11)/11 - 12150*
x^12

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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]

-12150*x^12-539460/11*x^11-348219/5*x^10-22695*x^9+85833/2*x^8+45531*x^7+13202/3
*x^6-78132/5*x^5-7800*x^4+2608/3*x^3+1824*x^2+576*x

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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]

-12150*x^12 - 539460/11*x^11 - 348219/5*x^10 - 22695*x^9 + 85833/2*x^8 + 45531*x
^7 + 13202/3*x^6 - 78132/5*x^5 - 7800*x^4 + 2608/3*x^3 + 1824*x^2 + 576*x

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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]

-12150*x^12 - 539460/11*x^11 - 348219/5*x^10 - 22695*x^9 + 85833/2*x^8 + 45531*x
^7 + 13202/3*x^6 - 78132/5*x^5 - 7800*x^4 + 2608/3*x^3 + 1824*x^2 + 576*x

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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]

-12150*x**12 - 539460*x**11/11 - 348219*x**10/5 - 22695*x**9 + 85833*x**8/2 + 45
531*x**7 + 13202*x**6/3 - 78132*x**5/5 - 7800*x**4 + 2608*x**3/3 + 1824*x**2 + 5
76*x

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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]

-12150*x^12 - 539460/11*x^11 - 348219/5*x^10 - 22695*x^9 + 85833/2*x^8 + 45531*x
^7 + 13202/3*x^6 - 78132/5*x^5 - 7800*x^4 + 2608/3*x^3 + 1824*x^2 + 576*x