3.1142 \(\int (1-2 x) (2+3 x)^7 (3+5 x)^2 \, dx\)

Optimal. Leaf size=45 \[ -\frac{50}{891} (3 x+2)^{11}+\frac{13}{54} (3 x+2)^{10}-\frac{8}{81} (3 x+2)^9+\frac{7}{648} (3 x+2)^8 \]

[Out]

(7*(2 + 3*x)^8)/648 - (8*(2 + 3*x)^9)/81 + (13*(2 + 3*x)^10)/54 - (50*(2 + 3*x)^
11)/891

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Rubi [A]  time = 0.0810706, antiderivative size = 45, 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 \[ -\frac{50}{891} (3 x+2)^{11}+\frac{13}{54} (3 x+2)^{10}-\frac{8}{81} (3 x+2)^9+\frac{7}{648} (3 x+2)^8 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)^2,x]

[Out]

(7*(2 + 3*x)^8)/648 - (8*(2 + 3*x)^9)/81 + (13*(2 + 3*x)^10)/54 - (50*(2 + 3*x)^
11)/891

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Rubi in Sympy [A]  time = 11.5677, size = 39, normalized size = 0.87 \[ - \frac{50 \left (3 x + 2\right )^{11}}{891} + \frac{13 \left (3 x + 2\right )^{10}}{54} - \frac{8 \left (3 x + 2\right )^{9}}{81} + \frac{7 \left (3 x + 2\right )^{8}}{648} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(2+3*x)**7*(3+5*x)**2,x)

[Out]

-50*(3*x + 2)**11/891 + 13*(3*x + 2)**10/54 - 8*(3*x + 2)**9/81 + 7*(3*x + 2)**8
/648

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Mathematica [A]  time = 0.0034107, size = 62, normalized size = 1.38 \[ -\frac{109350 x^{11}}{11}-\frac{117369 x^{10}}{2}-150174 x^9-\frac{1706265 x^8}{8}-173286 x^7-62622 x^6+21336 x^5+38804 x^4+\frac{66080 x^3}{3}+6816 x^2+1152 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)^2,x]

[Out]

1152*x + 6816*x^2 + (66080*x^3)/3 + 38804*x^4 + 21336*x^5 - 62622*x^6 - 173286*x
^7 - (1706265*x^8)/8 - 150174*x^9 - (117369*x^10)/2 - (109350*x^11)/11

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Maple [A]  time = 0.002, size = 55, normalized size = 1.2 \[ -{\frac{109350\,{x}^{11}}{11}}-{\frac{117369\,{x}^{10}}{2}}-150174\,{x}^{9}-{\frac{1706265\,{x}^{8}}{8}}-173286\,{x}^{7}-62622\,{x}^{6}+21336\,{x}^{5}+38804\,{x}^{4}+{\frac{66080\,{x}^{3}}{3}}+6816\,{x}^{2}+1152\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)^7*(3+5*x)^2,x)

[Out]

-109350/11*x^11-117369/2*x^10-150174*x^9-1706265/8*x^8-173286*x^7-62622*x^6+2133
6*x^5+38804*x^4+66080/3*x^3+6816*x^2+1152*x

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Maxima [A]  time = 1.34086, size = 73, normalized size = 1.62 \[ -\frac{109350}{11} \, x^{11} - \frac{117369}{2} \, x^{10} - 150174 \, x^{9} - \frac{1706265}{8} \, x^{8} - 173286 \, x^{7} - 62622 \, x^{6} + 21336 \, x^{5} + 38804 \, x^{4} + \frac{66080}{3} \, x^{3} + 6816 \, x^{2} + 1152 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(3*x + 2)^7*(2*x - 1),x, algorithm="maxima")

[Out]

-109350/11*x^11 - 117369/2*x^10 - 150174*x^9 - 1706265/8*x^8 - 173286*x^7 - 6262
2*x^6 + 21336*x^5 + 38804*x^4 + 66080/3*x^3 + 6816*x^2 + 1152*x

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Fricas [A]  time = 0.186066, size = 1, normalized size = 0.02 \[ -\frac{109350}{11} x^{11} - \frac{117369}{2} x^{10} - 150174 x^{9} - \frac{1706265}{8} x^{8} - 173286 x^{7} - 62622 x^{6} + 21336 x^{5} + 38804 x^{4} + \frac{66080}{3} x^{3} + 6816 x^{2} + 1152 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(3*x + 2)^7*(2*x - 1),x, algorithm="fricas")

[Out]

-109350/11*x^11 - 117369/2*x^10 - 150174*x^9 - 1706265/8*x^8 - 173286*x^7 - 6262
2*x^6 + 21336*x^5 + 38804*x^4 + 66080/3*x^3 + 6816*x^2 + 1152*x

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Sympy [A]  time = 0.118712, size = 60, normalized size = 1.33 \[ - \frac{109350 x^{11}}{11} - \frac{117369 x^{10}}{2} - 150174 x^{9} - \frac{1706265 x^{8}}{8} - 173286 x^{7} - 62622 x^{6} + 21336 x^{5} + 38804 x^{4} + \frac{66080 x^{3}}{3} + 6816 x^{2} + 1152 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(2+3*x)**7*(3+5*x)**2,x)

[Out]

-109350*x**11/11 - 117369*x**10/2 - 150174*x**9 - 1706265*x**8/8 - 173286*x**7 -
62622*x**6 + 21336*x**5 + 38804*x**4 + 66080*x**3/3 + 6816*x**2 + 1152*x

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GIAC/XCAS [A]  time = 0.212549, size = 73, normalized size = 1.62 \[ -\frac{109350}{11} \, x^{11} - \frac{117369}{2} \, x^{10} - 150174 \, x^{9} - \frac{1706265}{8} \, x^{8} - 173286 \, x^{7} - 62622 \, x^{6} + 21336 \, x^{5} + 38804 \, x^{4} + \frac{66080}{3} \, x^{3} + 6816 \, x^{2} + 1152 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(3*x + 2)^7*(2*x - 1),x, algorithm="giac")

[Out]

-109350/11*x^11 - 117369/2*x^10 - 150174*x^9 - 1706265/8*x^8 - 173286*x^7 - 6262
2*x^6 + 21336*x^5 + 38804*x^4 + 66080/3*x^3 + 6816*x^2 + 1152*x