3.1359 \(\int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx\)

Optimal. Leaf size=78 \[ -\frac{675}{256} (1-2 x)^{10}+\frac{1275}{32} (1-2 x)^9-\frac{260055 (1-2 x)^8}{1024}+\frac{98209}{112} (1-2 x)^7-\frac{444983}{256} (1-2 x)^6+\frac{302379}{160} (1-2 x)^5-\frac{456533}{512} (1-2 x)^4 \]

[Out]

(-456533*(1 - 2*x)^4)/512 + (302379*(1 - 2*x)^5)/160 - (444983*(1 - 2*x)^6)/256
+ (98209*(1 - 2*x)^7)/112 - (260055*(1 - 2*x)^8)/1024 + (1275*(1 - 2*x)^9)/32 -
(675*(1 - 2*x)^10)/256

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Rubi [A]  time = 0.101081, antiderivative size = 78, 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 \[ -\frac{675}{256} (1-2 x)^{10}+\frac{1275}{32} (1-2 x)^9-\frac{260055 (1-2 x)^8}{1024}+\frac{98209}{112} (1-2 x)^7-\frac{444983}{256} (1-2 x)^6+\frac{302379}{160} (1-2 x)^5-\frac{456533}{512} (1-2 x)^4 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^3,x]

[Out]

(-456533*(1 - 2*x)^4)/512 + (302379*(1 - 2*x)^5)/160 - (444983*(1 - 2*x)^6)/256
+ (98209*(1 - 2*x)^7)/112 - (260055*(1 - 2*x)^8)/1024 + (1275*(1 - 2*x)^9)/32 -
(675*(1 - 2*x)^10)/256

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 2700 x^{10} - 6900 x^{9} - \frac{14355 x^{8}}{4} + \frac{33013 x^{7}}{7} + \frac{10513 x^{6}}{2} - \frac{1419 x^{5}}{5} - \frac{8693 x^{4}}{4} - 534 x^{3} + 216 x + 756 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3*(2+3*x)**3*(3+5*x)**3,x)

[Out]

-2700*x**10 - 6900*x**9 - 14355*x**8/4 + 33013*x**7/7 + 10513*x**6/2 - 1419*x**5
/5 - 8693*x**4/4 - 534*x**3 + 216*x + 756*Integral(x, x)

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Mathematica [A]  time = 0.00416874, size = 59, normalized size = 0.76 \[ -2700 x^{10}-6900 x^9-\frac{14355 x^8}{4}+\frac{33013 x^7}{7}+\frac{10513 x^6}{2}-\frac{1419 x^5}{5}-\frac{8693 x^4}{4}-534 x^3+378 x^2+216 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^3,x]

[Out]

216*x + 378*x^2 - 534*x^3 - (8693*x^4)/4 - (1419*x^5)/5 + (10513*x^6)/2 + (33013
*x^7)/7 - (14355*x^8)/4 - 6900*x^9 - 2700*x^10

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Maple [A]  time = 0.001, size = 50, normalized size = 0.6 \[ -2700\,{x}^{10}-6900\,{x}^{9}-{\frac{14355\,{x}^{8}}{4}}+{\frac{33013\,{x}^{7}}{7}}+{\frac{10513\,{x}^{6}}{2}}-{\frac{1419\,{x}^{5}}{5}}-{\frac{8693\,{x}^{4}}{4}}-534\,{x}^{3}+378\,{x}^{2}+216\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(2+3*x)^3*(3+5*x)^3,x)

[Out]

-2700*x^10-6900*x^9-14355/4*x^8+33013/7*x^7+10513/2*x^6-1419/5*x^5-8693/4*x^4-53
4*x^3+378*x^2+216*x

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Maxima [A]  time = 1.35066, size = 66, normalized size = 0.85 \[ -2700 \, x^{10} - 6900 \, x^{9} - \frac{14355}{4} \, x^{8} + \frac{33013}{7} \, x^{7} + \frac{10513}{2} \, x^{6} - \frac{1419}{5} \, x^{5} - \frac{8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^3*(2*x - 1)^3,x, algorithm="maxima")

[Out]

-2700*x^10 - 6900*x^9 - 14355/4*x^8 + 33013/7*x^7 + 10513/2*x^6 - 1419/5*x^5 - 8
693/4*x^4 - 534*x^3 + 378*x^2 + 216*x

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Fricas [A]  time = 0.179252, size = 1, normalized size = 0.01 \[ -2700 x^{10} - 6900 x^{9} - \frac{14355}{4} x^{8} + \frac{33013}{7} x^{7} + \frac{10513}{2} x^{6} - \frac{1419}{5} x^{5} - \frac{8693}{4} x^{4} - 534 x^{3} + 378 x^{2} + 216 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^3*(2*x - 1)^3,x, algorithm="fricas")

[Out]

-2700*x^10 - 6900*x^9 - 14355/4*x^8 + 33013/7*x^7 + 10513/2*x^6 - 1419/5*x^5 - 8
693/4*x^4 - 534*x^3 + 378*x^2 + 216*x

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Sympy [A]  time = 0.109877, size = 56, normalized size = 0.72 \[ - 2700 x^{10} - 6900 x^{9} - \frac{14355 x^{8}}{4} + \frac{33013 x^{7}}{7} + \frac{10513 x^{6}}{2} - \frac{1419 x^{5}}{5} - \frac{8693 x^{4}}{4} - 534 x^{3} + 378 x^{2} + 216 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(2+3*x)**3*(3+5*x)**3,x)

[Out]

-2700*x**10 - 6900*x**9 - 14355*x**8/4 + 33013*x**7/7 + 10513*x**6/2 - 1419*x**5
/5 - 8693*x**4/4 - 534*x**3 + 378*x**2 + 216*x

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GIAC/XCAS [A]  time = 0.220359, size = 66, normalized size = 0.85 \[ -2700 \, x^{10} - 6900 \, x^{9} - \frac{14355}{4} \, x^{8} + \frac{33013}{7} \, x^{7} + \frac{10513}{2} \, x^{6} - \frac{1419}{5} \, x^{5} - \frac{8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^3*(2*x - 1)^3,x, algorithm="giac")

[Out]

-2700*x^10 - 6900*x^9 - 14355/4*x^8 + 33013/7*x^7 + 10513/2*x^6 - 1419/5*x^5 - 8
693/4*x^4 - 534*x^3 + 378*x^2 + 216*x