3.1358 \(\int (1-2 x)^3 (2+3 x)^4 (3+5 x)^3 \, dx\)

Optimal. Leaf size=78 \[ -\frac{1000 (3 x+2)^{11}}{24057}+\frac{370}{729} (3 x+2)^{10}-\frac{14390 (3 x+2)^9}{6561}+\frac{66193 (3 x+2)^8}{17496}-\frac{1439}{729} (3 x+2)^7+\frac{1813 (3 x+2)^6}{4374}-\frac{343 (3 x+2)^5}{10935} \]

[Out]

(-343*(2 + 3*x)^5)/10935 + (1813*(2 + 3*x)^6)/4374 - (1439*(2 + 3*x)^7)/729 + (6
6193*(2 + 3*x)^8)/17496 - (14390*(2 + 3*x)^9)/6561 + (370*(2 + 3*x)^10)/729 - (1
000*(2 + 3*x)^11)/24057

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Rubi [A]  time = 0.106548, 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 \[ -\frac{1000 (3 x+2)^{11}}{24057}+\frac{370}{729} (3 x+2)^{10}-\frac{14390 (3 x+2)^9}{6561}+\frac{66193 (3 x+2)^8}{17496}-\frac{1439}{729} (3 x+2)^7+\frac{1813 (3 x+2)^6}{4374}-\frac{343 (3 x+2)^5}{10935} \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3,x]

[Out]

(-343*(2 + 3*x)^5)/10935 + (1813*(2 + 3*x)^6)/4374 - (1439*(2 + 3*x)^7)/729 + (6
6193*(2 + 3*x)^8)/17496 - (14390*(2 + 3*x)^9)/6561 + (370*(2 + 3*x)^10)/729 - (1
000*(2 + 3*x)^11)/24057

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{81000 x^{11}}{11} - 24030 x^{10} - 23370 x^{9} + \frac{41619 x^{8}}{8} + 22949 x^{7} + \frac{19607 x^{6}}{2} - \frac{28917 x^{5}}{5} - 5548 x^{4} - 312 x^{3} + 432 x + 2160 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3*(2+3*x)**4*(3+5*x)**3,x)

[Out]

-81000*x**11/11 - 24030*x**10 - 23370*x**9 + 41619*x**8/8 + 22949*x**7 + 19607*x
**6/2 - 28917*x**5/5 - 5548*x**4 - 312*x**3 + 432*x + 2160*Integral(x, x)

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Mathematica [A]  time = 0.00425865, size = 62, normalized size = 0.79 \[ -\frac{81000 x^{11}}{11}-24030 x^{10}-23370 x^9+\frac{41619 x^8}{8}+22949 x^7+\frac{19607 x^6}{2}-\frac{28917 x^5}{5}-5548 x^4-312 x^3+1080 x^2+432 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3,x]

[Out]

432*x + 1080*x^2 - 312*x^3 - 5548*x^4 - (28917*x^5)/5 + (19607*x^6)/2 + 22949*x^
7 + (41619*x^8)/8 - 23370*x^9 - 24030*x^10 - (81000*x^11)/11

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Maple [A]  time = 0.001, size = 55, normalized size = 0.7 \[ -{\frac{81000\,{x}^{11}}{11}}-24030\,{x}^{10}-23370\,{x}^{9}+{\frac{41619\,{x}^{8}}{8}}+22949\,{x}^{7}+{\frac{19607\,{x}^{6}}{2}}-{\frac{28917\,{x}^{5}}{5}}-5548\,{x}^{4}-312\,{x}^{3}+1080\,{x}^{2}+432\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x)

[Out]

-81000/11*x^11-24030*x^10-23370*x^9+41619/8*x^8+22949*x^7+19607/2*x^6-28917/5*x^
5-5548*x^4-312*x^3+1080*x^2+432*x

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Maxima [A]  time = 1.34334, size = 73, normalized size = 0.94 \[ -\frac{81000}{11} \, x^{11} - 24030 \, x^{10} - 23370 \, x^{9} + \frac{41619}{8} \, x^{8} + 22949 \, x^{7} + \frac{19607}{2} \, x^{6} - \frac{28917}{5} \, x^{5} - 5548 \, x^{4} - 312 \, x^{3} + 1080 \, x^{2} + 432 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^3,x, algorithm="maxima")

[Out]

-81000/11*x^11 - 24030*x^10 - 23370*x^9 + 41619/8*x^8 + 22949*x^7 + 19607/2*x^6
- 28917/5*x^5 - 5548*x^4 - 312*x^3 + 1080*x^2 + 432*x

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Fricas [A]  time = 0.180595, size = 1, normalized size = 0.01 \[ -\frac{81000}{11} x^{11} - 24030 x^{10} - 23370 x^{9} + \frac{41619}{8} x^{8} + 22949 x^{7} + \frac{19607}{2} x^{6} - \frac{28917}{5} x^{5} - 5548 x^{4} - 312 x^{3} + 1080 x^{2} + 432 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^3,x, algorithm="fricas")

[Out]

-81000/11*x^11 - 24030*x^10 - 23370*x^9 + 41619/8*x^8 + 22949*x^7 + 19607/2*x^6
- 28917/5*x^5 - 5548*x^4 - 312*x^3 + 1080*x^2 + 432*x

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Sympy [A]  time = 0.125126, size = 60, normalized size = 0.77 \[ - \frac{81000 x^{11}}{11} - 24030 x^{10} - 23370 x^{9} + \frac{41619 x^{8}}{8} + 22949 x^{7} + \frac{19607 x^{6}}{2} - \frac{28917 x^{5}}{5} - 5548 x^{4} - 312 x^{3} + 1080 x^{2} + 432 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(2+3*x)**4*(3+5*x)**3,x)

[Out]

-81000*x**11/11 - 24030*x**10 - 23370*x**9 + 41619*x**8/8 + 22949*x**7 + 19607*x
**6/2 - 28917*x**5/5 - 5548*x**4 - 312*x**3 + 1080*x**2 + 432*x

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GIAC/XCAS [A]  time = 0.209335, size = 73, normalized size = 0.94 \[ -\frac{81000}{11} \, x^{11} - 24030 \, x^{10} - 23370 \, x^{9} + \frac{41619}{8} \, x^{8} + 22949 \, x^{7} + \frac{19607}{2} \, x^{6} - \frac{28917}{5} \, x^{5} - 5548 \, x^{4} - 312 \, x^{3} + 1080 \, x^{2} + 432 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^3,x, algorithm="giac")

[Out]

-81000/11*x^11 - 24030*x^10 - 23370*x^9 + 41619/8*x^8 + 22949*x^7 + 19607/2*x^6
- 28917/5*x^5 - 5548*x^4 - 312*x^3 + 1080*x^2 + 432*x