3.1343 \(\int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx\)

Optimal. Leaf size=67 \[ \frac{75}{64} (1-2 x)^9-\frac{7695}{512} (1-2 x)^8+\frac{17541}{224} (1-2 x)^7-\frac{39977}{192} (1-2 x)^6+\frac{91091}{320} (1-2 x)^5-\frac{41503}{256} (1-2 x)^4 \]

[Out]

(-41503*(1 - 2*x)^4)/256 + (91091*(1 - 2*x)^5)/320 - (39977*(1 - 2*x)^6)/192 + (
17541*(1 - 2*x)^7)/224 - (7695*(1 - 2*x)^8)/512 + (75*(1 - 2*x)^9)/64

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Rubi [A]  time = 0.0930933, 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 \[ \frac{75}{64} (1-2 x)^9-\frac{7695}{512} (1-2 x)^8+\frac{17541}{224} (1-2 x)^7-\frac{39977}{192} (1-2 x)^6+\frac{91091}{320} (1-2 x)^5-\frac{41503}{256} (1-2 x)^4 \]

Antiderivative was successfully verified.

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

[Out]

(-41503*(1 - 2*x)^4)/256 + (91091*(1 - 2*x)^5)/320 - (39977*(1 - 2*x)^6)/192 + (
17541*(1 - 2*x)^7)/224 - (7695*(1 - 2*x)^8)/512 + (75*(1 - 2*x)^9)/64

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 600 x^{9} - \frac{2295 x^{8}}{2} - \frac{234 x^{7}}{7} + \frac{6743 x^{6}}{6} + \frac{2262 x^{5}}{5} - \frac{1641 x^{4}}{4} - \frac{754 x^{3}}{3} + 72 x + 132 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600*x**9 - 2295*x**8/2 - 234*x**7/7 + 6743*x**6/6 + 2262*x**5/5 - 1641*x**4/4 -
754*x**3/3 + 72*x + 132*Integral(x, x)

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Mathematica [A]  time = 0.00415018, size = 56, normalized size = 0.84 \[ -600 x^9-\frac{2295 x^8}{2}-\frac{234 x^7}{7}+\frac{6743 x^6}{6}+\frac{2262 x^5}{5}-\frac{1641 x^4}{4}-\frac{754 x^3}{3}+66 x^2+72 x \]

Antiderivative was successfully verified.

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

[Out]

72*x + 66*x^2 - (754*x^3)/3 - (1641*x^4)/4 + (2262*x^5)/5 + (6743*x^6)/6 - (234*
x^7)/7 - (2295*x^8)/2 - 600*x^9

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Maple [A]  time = 0., size = 45, normalized size = 0.7 \[ -600\,{x}^{9}-{\frac{2295\,{x}^{8}}{2}}-{\frac{234\,{x}^{7}}{7}}+{\frac{6743\,{x}^{6}}{6}}+{\frac{2262\,{x}^{5}}{5}}-{\frac{1641\,{x}^{4}}{4}}-{\frac{754\,{x}^{3}}{3}}+66\,{x}^{2}+72\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600*x^9-2295/2*x^8-234/7*x^7+6743/6*x^6+2262/5*x^5-1641/4*x^4-754/3*x^3+66*x^2+
72*x

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Maxima [A]  time = 1.34611, size = 59, normalized size = 0.88 \[ -600 \, x^{9} - \frac{2295}{2} \, x^{8} - \frac{234}{7} \, x^{7} + \frac{6743}{6} \, x^{6} + \frac{2262}{5} \, x^{5} - \frac{1641}{4} \, x^{4} - \frac{754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600*x^9 - 2295/2*x^8 - 234/7*x^7 + 6743/6*x^6 + 2262/5*x^5 - 1641/4*x^4 - 754/3
*x^3 + 66*x^2 + 72*x

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Fricas [A]  time = 0.184615, size = 1, normalized size = 0.01 \[ -600 x^{9} - \frac{2295}{2} x^{8} - \frac{234}{7} x^{7} + \frac{6743}{6} x^{6} + \frac{2262}{5} x^{5} - \frac{1641}{4} x^{4} - \frac{754}{3} x^{3} + 66 x^{2} + 72 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600*x^9 - 2295/2*x^8 - 234/7*x^7 + 6743/6*x^6 + 2262/5*x^5 - 1641/4*x^4 - 754/3
*x^3 + 66*x^2 + 72*x

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Sympy [A]  time = 0.100571, size = 53, normalized size = 0.79 \[ - 600 x^{9} - \frac{2295 x^{8}}{2} - \frac{234 x^{7}}{7} + \frac{6743 x^{6}}{6} + \frac{2262 x^{5}}{5} - \frac{1641 x^{4}}{4} - \frac{754 x^{3}}{3} + 66 x^{2} + 72 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600*x**9 - 2295*x**8/2 - 234*x**7/7 + 6743*x**6/6 + 2262*x**5/5 - 1641*x**4/4 -
754*x**3/3 + 66*x**2 + 72*x

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GIAC/XCAS [A]  time = 0.207004, size = 59, normalized size = 0.88 \[ -600 \, x^{9} - \frac{2295}{2} \, x^{8} - \frac{234}{7} \, x^{7} + \frac{6743}{6} \, x^{6} + \frac{2262}{5} \, x^{5} - \frac{1641}{4} \, x^{4} - \frac{754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600*x^9 - 2295/2*x^8 - 234/7*x^7 + 6743/6*x^6 + 2262/5*x^5 - 1641/4*x^4 - 754/3
*x^3 + 66*x^2 + 72*x