3.1160 \(\int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx\)

Optimal. Leaf size=56 \[ -\frac{250 (3 x+2)^{11}}{2673}+\frac{205}{486} (3 x+2)^{10}-\frac{185}{729} (3 x+2)^9+\frac{107 (3 x+2)^8}{1944}-\frac{1}{243} (3 x+2)^7 \]

[Out]

-(2 + 3*x)^7/243 + (107*(2 + 3*x)^8)/1944 - (185*(2 + 3*x)^9)/729 + (205*(2 + 3*
x)^10)/486 - (250*(2 + 3*x)^11)/2673

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Rubi [A]  time = 0.0804876, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{250 (3 x+2)^{11}}{2673}+\frac{205}{486} (3 x+2)^{10}-\frac{185}{729} (3 x+2)^9+\frac{107 (3 x+2)^8}{1944}-\frac{1}{243} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^3,x]

[Out]

-(2 + 3*x)^7/243 + (107*(2 + 3*x)^8)/1944 - (185*(2 + 3*x)^9)/729 + (205*(2 + 3*
x)^10)/486 - (250*(2 + 3*x)^11)/2673

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Rubi in Sympy [A]  time = 12.4394, size = 48, normalized size = 0.86 \[ - \frac{250 \left (3 x + 2\right )^{11}}{2673} + \frac{205 \left (3 x + 2\right )^{10}}{486} - \frac{185 \left (3 x + 2\right )^{9}}{729} + \frac{107 \left (3 x + 2\right )^{8}}{1944} - \frac{\left (3 x + 2\right )^{7}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(2+3*x)**6*(3+5*x)**3,x)

[Out]

-250*(3*x + 2)**11/2673 + 205*(3*x + 2)**10/486 - 185*(3*x + 2)**9/729 + 107*(3*
x + 2)**8/1944 - (3*x + 2)**7/243

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Mathematica [A]  time = 0.00331502, size = 60, normalized size = 1.07 \[ -\frac{182250 x^{11}}{11}-\frac{193185 x^{10}}{2}-243945 x^9-\frac{2731671 x^8}{8}-272403 x^7-94668 x^6+36148 x^5+61220 x^4+34032 x^3+10368 x^2+1728 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^3,x]

[Out]

1728*x + 10368*x^2 + 34032*x^3 + 61220*x^4 + 36148*x^5 - 94668*x^6 - 272403*x^7
- (2731671*x^8)/8 - 243945*x^9 - (193185*x^10)/2 - (182250*x^11)/11

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Maple [A]  time = 0.001, size = 55, normalized size = 1. \[ -{\frac{182250\,{x}^{11}}{11}}-{\frac{193185\,{x}^{10}}{2}}-243945\,{x}^{9}-{\frac{2731671\,{x}^{8}}{8}}-272403\,{x}^{7}-94668\,{x}^{6}+36148\,{x}^{5}+61220\,{x}^{4}+34032\,{x}^{3}+10368\,{x}^{2}+1728\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)^6*(3+5*x)^3,x)

[Out]

-182250/11*x^11-193185/2*x^10-243945*x^9-2731671/8*x^8-272403*x^7-94668*x^6+3614
8*x^5+61220*x^4+34032*x^3+10368*x^2+1728*x

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Maxima [A]  time = 1.34918, size = 73, normalized size = 1.3 \[ -\frac{182250}{11} \, x^{11} - \frac{193185}{2} \, x^{10} - 243945 \, x^{9} - \frac{2731671}{8} \, x^{8} - 272403 \, x^{7} - 94668 \, x^{6} + 36148 \, x^{5} + 61220 \, x^{4} + 34032 \, x^{3} + 10368 \, x^{2} + 1728 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^6*(2*x - 1),x, algorithm="maxima")

[Out]

-182250/11*x^11 - 193185/2*x^10 - 243945*x^9 - 2731671/8*x^8 - 272403*x^7 - 9466
8*x^6 + 36148*x^5 + 61220*x^4 + 34032*x^3 + 10368*x^2 + 1728*x

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Fricas [A]  time = 0.177257, size = 1, normalized size = 0.02 \[ -\frac{182250}{11} x^{11} - \frac{193185}{2} x^{10} - 243945 x^{9} - \frac{2731671}{8} x^{8} - 272403 x^{7} - 94668 x^{6} + 36148 x^{5} + 61220 x^{4} + 34032 x^{3} + 10368 x^{2} + 1728 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^6*(2*x - 1),x, algorithm="fricas")

[Out]

-182250/11*x^11 - 193185/2*x^10 - 243945*x^9 - 2731671/8*x^8 - 272403*x^7 - 9466
8*x^6 + 36148*x^5 + 61220*x^4 + 34032*x^3 + 10368*x^2 + 1728*x

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Sympy [A]  time = 0.111113, size = 58, normalized size = 1.04 \[ - \frac{182250 x^{11}}{11} - \frac{193185 x^{10}}{2} - 243945 x^{9} - \frac{2731671 x^{8}}{8} - 272403 x^{7} - 94668 x^{6} + 36148 x^{5} + 61220 x^{4} + 34032 x^{3} + 10368 x^{2} + 1728 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(2+3*x)**6*(3+5*x)**3,x)

[Out]

-182250*x**11/11 - 193185*x**10/2 - 243945*x**9 - 2731671*x**8/8 - 272403*x**7 -
94668*x**6 + 36148*x**5 + 61220*x**4 + 34032*x**3 + 10368*x**2 + 1728*x

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GIAC/XCAS [A]  time = 0.20793, size = 73, normalized size = 1.3 \[ -\frac{182250}{11} \, x^{11} - \frac{193185}{2} \, x^{10} - 243945 \, x^{9} - \frac{2731671}{8} \, x^{8} - 272403 \, x^{7} - 94668 \, x^{6} + 36148 \, x^{5} + 61220 \, x^{4} + 34032 \, x^{3} + 10368 \, x^{2} + 1728 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^6*(2*x - 1),x, algorithm="giac")

[Out]

-182250/11*x^11 - 193185/2*x^10 - 243945*x^9 - 2731671/8*x^8 - 272403*x^7 - 9466
8*x^6 + 36148*x^5 + 61220*x^4 + 34032*x^3 + 10368*x^2 + 1728*x