3.1258 \(\int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{500 (3 x+2)^{11}}{8019}-\frac{380}{729} (3 x+2)^{10}+\frac{8285 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{5832}+\frac{109}{729} (3 x+2)^7-\frac{49 (3 x+2)^6}{4374} \]

[Out]

(-49*(2 + 3*x)^6)/4374 + (109*(2 + 3*x)^7)/729 - (4099*(2 + 3*x)^8)/5832 + (8285
*(2 + 3*x)^9)/6561 - (380*(2 + 3*x)^10)/729 + (500*(2 + 3*x)^11)/8019

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Rubi [A]  time = 0.100915, antiderivative size = 67, 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 \[ \frac{500 (3 x+2)^{11}}{8019}-\frac{380}{729} (3 x+2)^{10}+\frac{8285 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{5832}+\frac{109}{729} (3 x+2)^7-\frac{49 (3 x+2)^6}{4374} \]

Antiderivative was successfully verified.

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

[Out]

(-49*(2 + 3*x)^6)/4374 + (109*(2 + 3*x)^7)/729 - (4099*(2 + 3*x)^8)/5832 + (8285
*(2 + 3*x)^9)/6561 - (380*(2 + 3*x)^10)/729 + (500*(2 + 3*x)^11)/8019

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{121500 x^{11}}{11} + 50220 x^{10} + 89655 x^{9} + \frac{551349 x^{8}}{8} - 987 x^{7} - \frac{252329 x^{6}}{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 864 x + 7344 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121500*x**11/11 + 50220*x**10 + 89655*x**9 + 551349*x**8/8 - 987*x**7 - 252329*x
**6/6 - 28322*x**5 - 2150*x**4 + 6432*x**3 + 864*x + 7344*Integral(x, x)

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Mathematica [A]  time = 0.00401323, size = 60, normalized size = 0.9 \[ \frac{121500 x^{11}}{11}+50220 x^{10}+89655 x^9+\frac{551349 x^8}{8}-987 x^7-\frac{252329 x^6}{6}-28322 x^5-2150 x^4+6432 x^3+3672 x^2+864 x \]

Antiderivative was successfully verified.

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

[Out]

864*x + 3672*x^2 + 6432*x^3 - 2150*x^4 - 28322*x^5 - (252329*x^6)/6 - 987*x^7 +
(551349*x^8)/8 + 89655*x^9 + 50220*x^10 + (121500*x^11)/11

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Maple [A]  time = 0.003, size = 55, normalized size = 0.8 \[{\frac{121500\,{x}^{11}}{11}}+50220\,{x}^{10}+89655\,{x}^{9}+{\frac{551349\,{x}^{8}}{8}}-987\,{x}^{7}-{\frac{252329\,{x}^{6}}{6}}-28322\,{x}^{5}-2150\,{x}^{4}+6432\,{x}^{3}+3672\,{x}^{2}+864\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121500/11*x^11+50220*x^10+89655*x^9+551349/8*x^8-987*x^7-252329/6*x^6-28322*x^5-
2150*x^4+6432*x^3+3672*x^2+864*x

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Maxima [A]  time = 1.34708, size = 73, normalized size = 1.09 \[ \frac{121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac{551349}{8} \, x^{8} - 987 \, x^{7} - \frac{252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121500/11*x^11 + 50220*x^10 + 89655*x^9 + 551349/8*x^8 - 987*x^7 - 252329/6*x^6
- 28322*x^5 - 2150*x^4 + 6432*x^3 + 3672*x^2 + 864*x

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Fricas [A]  time = 0.180019, size = 1, normalized size = 0.01 \[ \frac{121500}{11} x^{11} + 50220 x^{10} + 89655 x^{9} + \frac{551349}{8} x^{8} - 987 x^{7} - \frac{252329}{6} x^{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121500/11*x^11 + 50220*x^10 + 89655*x^9 + 551349/8*x^8 - 987*x^7 - 252329/6*x^6
- 28322*x^5 - 2150*x^4 + 6432*x^3 + 3672*x^2 + 864*x

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Sympy [A]  time = 0.118182, size = 58, normalized size = 0.87 \[ \frac{121500 x^{11}}{11} + 50220 x^{10} + 89655 x^{9} + \frac{551349 x^{8}}{8} - 987 x^{7} - \frac{252329 x^{6}}{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121500*x**11/11 + 50220*x**10 + 89655*x**9 + 551349*x**8/8 - 987*x**7 - 252329*x
**6/6 - 28322*x**5 - 2150*x**4 + 6432*x**3 + 3672*x**2 + 864*x

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GIAC/XCAS [A]  time = 0.218336, size = 73, normalized size = 1.09 \[ \frac{121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac{551349}{8} \, x^{8} - 987 \, x^{7} - \frac{252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121500/11*x^11 + 50220*x^10 + 89655*x^9 + 551349/8*x^8 - 987*x^7 - 252329/6*x^6
- 28322*x^5 - 2150*x^4 + 6432*x^3 + 3672*x^2 + 864*x