3.1141 \(\int (1-2 x) (2+3 x)^8 (3+5 x)^2 \, dx\)

Optimal. Leaf size=45 \[ -\frac{25}{486} (3 x+2)^{12}+\frac{65}{297} (3 x+2)^{11}-\frac{4}{45} (3 x+2)^{10}+\frac{7}{729} (3 x+2)^9 \]

[Out]

(7*(2 + 3*x)^9)/729 - (4*(2 + 3*x)^10)/45 + (65*(2 + 3*x)^11)/297 - (25*(2 + 3*x
)^12)/486

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Rubi [A]  time = 0.0885457, 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 \[ -\frac{25}{486} (3 x+2)^{12}+\frac{65}{297} (3 x+2)^{11}-\frac{4}{45} (3 x+2)^{10}+\frac{7}{729} (3 x+2)^9 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^2,x]

[Out]

(7*(2 + 3*x)^9)/729 - (4*(2 + 3*x)^10)/45 + (65*(2 + 3*x)^11)/297 - (25*(2 + 3*x
)^12)/486

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Rubi in Sympy [A]  time = 12.3004, size = 39, normalized size = 0.87 \[ - \frac{25 \left (3 x + 2\right )^{12}}{486} + \frac{65 \left (3 x + 2\right )^{11}}{297} - \frac{4 \left (3 x + 2\right )^{10}}{45} + \frac{7 \left (3 x + 2\right )^{9}}{729} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(2+3*x)**8*(3+5*x)**2,x)

[Out]

-25*(3*x + 2)**12/486 + 65*(3*x + 2)**11/297 - 4*(3*x + 2)**10/45 + 7*(3*x + 2)*
*9/729

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Mathematica [A]  time = 0.00356973, size = 69, normalized size = 1.53 \[ -\frac{54675 x^{12}}{2}-\frac{1979235 x^{11}}{11}-\frac{2614194 x^{10}}{5}-869103 x^9-881442 x^8-507600 x^7-71904 x^6+\frac{679008 x^5}{5}+127168 x^4+\frac{173056 x^3}{3}+15360 x^2+2304 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^2,x]

[Out]

2304*x + 15360*x^2 + (173056*x^3)/3 + 127168*x^4 + (679008*x^5)/5 - 71904*x^6 -
507600*x^7 - 881442*x^8 - 869103*x^9 - (2614194*x^10)/5 - (1979235*x^11)/11 - (5
4675*x^12)/2

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Maple [A]  time = 0.003, size = 60, normalized size = 1.3 \[ -{\frac{54675\,{x}^{12}}{2}}-{\frac{1979235\,{x}^{11}}{11}}-{\frac{2614194\,{x}^{10}}{5}}-869103\,{x}^{9}-881442\,{x}^{8}-507600\,{x}^{7}-71904\,{x}^{6}+{\frac{679008\,{x}^{5}}{5}}+127168\,{x}^{4}+{\frac{173056\,{x}^{3}}{3}}+15360\,{x}^{2}+2304\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)^8*(3+5*x)^2,x)

[Out]

-54675/2*x^12-1979235/11*x^11-2614194/5*x^10-869103*x^9-881442*x^8-507600*x^7-71
904*x^6+679008/5*x^5+127168*x^4+173056/3*x^3+15360*x^2+2304*x

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Maxima [A]  time = 1.3433, size = 80, normalized size = 1.78 \[ -\frac{54675}{2} \, x^{12} - \frac{1979235}{11} \, x^{11} - \frac{2614194}{5} \, x^{10} - 869103 \, x^{9} - 881442 \, x^{8} - 507600 \, x^{7} - 71904 \, x^{6} + \frac{679008}{5} \, x^{5} + 127168 \, x^{4} + \frac{173056}{3} \, x^{3} + 15360 \, x^{2} + 2304 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(3*x + 2)^8*(2*x - 1),x, algorithm="maxima")

[Out]

-54675/2*x^12 - 1979235/11*x^11 - 2614194/5*x^10 - 869103*x^9 - 881442*x^8 - 507
600*x^7 - 71904*x^6 + 679008/5*x^5 + 127168*x^4 + 173056/3*x^3 + 15360*x^2 + 230
4*x

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Fricas [A]  time = 0.186324, size = 1, normalized size = 0.02 \[ -\frac{54675}{2} x^{12} - \frac{1979235}{11} x^{11} - \frac{2614194}{5} x^{10} - 869103 x^{9} - 881442 x^{8} - 507600 x^{7} - 71904 x^{6} + \frac{679008}{5} x^{5} + 127168 x^{4} + \frac{173056}{3} x^{3} + 15360 x^{2} + 2304 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(3*x + 2)^8*(2*x - 1),x, algorithm="fricas")

[Out]

-54675/2*x^12 - 1979235/11*x^11 - 2614194/5*x^10 - 869103*x^9 - 881442*x^8 - 507
600*x^7 - 71904*x^6 + 679008/5*x^5 + 127168*x^4 + 173056/3*x^3 + 15360*x^2 + 230
4*x

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Sympy [A]  time = 0.128677, size = 66, normalized size = 1.47 \[ - \frac{54675 x^{12}}{2} - \frac{1979235 x^{11}}{11} - \frac{2614194 x^{10}}{5} - 869103 x^{9} - 881442 x^{8} - 507600 x^{7} - 71904 x^{6} + \frac{679008 x^{5}}{5} + 127168 x^{4} + \frac{173056 x^{3}}{3} + 15360 x^{2} + 2304 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(2+3*x)**8*(3+5*x)**2,x)

[Out]

-54675*x**12/2 - 1979235*x**11/11 - 2614194*x**10/5 - 869103*x**9 - 881442*x**8
- 507600*x**7 - 71904*x**6 + 679008*x**5/5 + 127168*x**4 + 173056*x**3/3 + 15360
*x**2 + 2304*x

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GIAC/XCAS [A]  time = 0.209611, size = 80, normalized size = 1.78 \[ -\frac{54675}{2} \, x^{12} - \frac{1979235}{11} \, x^{11} - \frac{2614194}{5} \, x^{10} - 869103 \, x^{9} - 881442 \, x^{8} - 507600 \, x^{7} - 71904 \, x^{6} + \frac{679008}{5} \, x^{5} + 127168 \, x^{4} + \frac{173056}{3} \, x^{3} + 15360 \, x^{2} + 2304 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(3*x + 2)^8*(2*x - 1),x, algorithm="giac")

[Out]

-54675/2*x^12 - 1979235/11*x^11 - 2614194/5*x^10 - 869103*x^9 - 881442*x^8 - 507
600*x^7 - 71904*x^6 + 679008/5*x^5 + 127168*x^4 + 173056/3*x^3 + 15360*x^2 + 230
4*x