3.1225 \(\int (1-2 x)^2 (2+3 x)^2 (3+5 x) \, dx\)

Optimal. Leaf size=45 \[ \frac{15}{32} (1-2 x)^6-\frac{309}{80} (1-2 x)^5+\frac{707}{64} (1-2 x)^4-\frac{539}{48} (1-2 x)^3 \]

[Out]

(-539*(1 - 2*x)^3)/48 + (707*(1 - 2*x)^4)/64 - (309*(1 - 2*x)^5)/80 + (15*(1 - 2
*x)^6)/32

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Rubi [A]  time = 0.0612956, 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 \[ \frac{15}{32} (1-2 x)^6-\frac{309}{80} (1-2 x)^5+\frac{707}{64} (1-2 x)^4-\frac{539}{48} (1-2 x)^3 \]

Antiderivative was successfully verified.

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

[Out]

(-539*(1 - 2*x)^3)/48 + (707*(1 - 2*x)^4)/64 - (309*(1 - 2*x)^5)/80 + (15*(1 - 2
*x)^6)/32

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ 30 x^{6} + \frac{168 x^{5}}{5} - \frac{79 x^{4}}{4} - \frac{89 x^{3}}{3} + 12 x + 8 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

30*x**6 + 168*x**5/5 - 79*x**4/4 - 89*x**3/3 + 12*x + 8*Integral(x, x)

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Mathematica [A]  time = 0.00246835, size = 35, normalized size = 0.78 \[ 30 x^6+\frac{168 x^5}{5}-\frac{79 x^4}{4}-\frac{89 x^3}{3}+4 x^2+12 x \]

Antiderivative was successfully verified.

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

[Out]

12*x + 4*x^2 - (89*x^3)/3 - (79*x^4)/4 + (168*x^5)/5 + 30*x^6

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Maple [A]  time = 0., size = 30, normalized size = 0.7 \[ 30\,{x}^{6}+{\frac{168\,{x}^{5}}{5}}-{\frac{79\,{x}^{4}}{4}}-{\frac{89\,{x}^{3}}{3}}+4\,{x}^{2}+12\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

30*x^6+168/5*x^5-79/4*x^4-89/3*x^3+4*x^2+12*x

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Maxima [A]  time = 1.34495, size = 39, normalized size = 0.87 \[ 30 \, x^{6} + \frac{168}{5} \, x^{5} - \frac{79}{4} \, x^{4} - \frac{89}{3} \, x^{3} + 4 \, x^{2} + 12 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

30*x^6 + 168/5*x^5 - 79/4*x^4 - 89/3*x^3 + 4*x^2 + 12*x

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Fricas [A]  time = 0.18647, size = 1, normalized size = 0.02 \[ 30 x^{6} + \frac{168}{5} x^{5} - \frac{79}{4} x^{4} - \frac{89}{3} x^{3} + 4 x^{2} + 12 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

30*x^6 + 168/5*x^5 - 79/4*x^4 - 89/3*x^3 + 4*x^2 + 12*x

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Sympy [A]  time = 0.079627, size = 32, normalized size = 0.71 \[ 30 x^{6} + \frac{168 x^{5}}{5} - \frac{79 x^{4}}{4} - \frac{89 x^{3}}{3} + 4 x^{2} + 12 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

30*x**6 + 168*x**5/5 - 79*x**4/4 - 89*x**3/3 + 4*x**2 + 12*x

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GIAC/XCAS [A]  time = 0.205156, size = 39, normalized size = 0.87 \[ 30 \, x^{6} + \frac{168}{5} \, x^{5} - \frac{79}{4} \, x^{4} - \frac{89}{3} \, x^{3} + 4 \, x^{2} + 12 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

30*x^6 + 168/5*x^5 - 79/4*x^4 - 89/3*x^3 + 4*x^2 + 12*x