3.1344 \(\int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ -\frac{225}{256} (1-2 x)^8+\frac{255}{28} (1-2 x)^7-\frac{3467}{96} (1-2 x)^6+\frac{1309}{20} (1-2 x)^5-\frac{5929}{128} (1-2 x)^4 \]

[Out]

(-5929*(1 - 2*x)^4)/128 + (1309*(1 - 2*x)^5)/20 - (3467*(1 - 2*x)^6)/96 + (255*(
1 - 2*x)^7)/28 - (225*(1 - 2*x)^8)/256

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Rubi [A]  time = 0.0851913, antiderivative size = 56, 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 \[ -\frac{225}{256} (1-2 x)^8+\frac{255}{28} (1-2 x)^7-\frac{3467}{96} (1-2 x)^6+\frac{1309}{20} (1-2 x)^5-\frac{5929}{128} (1-2 x)^4 \]

Antiderivative was successfully verified.

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

[Out]

(-5929*(1 - 2*x)^4)/128 + (1309*(1 - 2*x)^5)/20 - (3467*(1 - 2*x)^6)/96 + (255*(
1 - 2*x)^7)/28 - (225*(1 - 2*x)^8)/256

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 225 x^{8} - \frac{1860 x^{7}}{7} + \frac{581 x^{6}}{3} + \frac{1473 x^{5}}{5} - 57 x^{4} - \frac{395 x^{3}}{3} + 36 x + 12 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x**8 - 1860*x**7/7 + 581*x**6/3 + 1473*x**5/5 - 57*x**4 - 395*x**3/3 + 36*x
+ 12*Integral(x, x)

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Mathematica [A]  time = 0.00229076, size = 47, normalized size = 0.84 \[ -225 x^8-\frac{1860 x^7}{7}+\frac{581 x^6}{3}+\frac{1473 x^5}{5}-57 x^4-\frac{395 x^3}{3}+6 x^2+36 x \]

Antiderivative was successfully verified.

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

[Out]

36*x + 6*x^2 - (395*x^3)/3 - 57*x^4 + (1473*x^5)/5 + (581*x^6)/3 - (1860*x^7)/7
- 225*x^8

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Maple [A]  time = 0.003, size = 40, normalized size = 0.7 \[ -225\,{x}^{8}-{\frac{1860\,{x}^{7}}{7}}+{\frac{581\,{x}^{6}}{3}}+{\frac{1473\,{x}^{5}}{5}}-57\,{x}^{4}-{\frac{395\,{x}^{3}}{3}}+6\,{x}^{2}+36\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x^8-1860/7*x^7+581/3*x^6+1473/5*x^5-57*x^4-395/3*x^3+6*x^2+36*x

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Maxima [A]  time = 1.35201, size = 53, normalized size = 0.95 \[ -225 \, x^{8} - \frac{1860}{7} \, x^{7} + \frac{581}{3} \, x^{6} + \frac{1473}{5} \, x^{5} - 57 \, x^{4} - \frac{395}{3} \, x^{3} + 6 \, x^{2} + 36 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x^8 - 1860/7*x^7 + 581/3*x^6 + 1473/5*x^5 - 57*x^4 - 395/3*x^3 + 6*x^2 + 36
*x

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Fricas [A]  time = 0.182544, size = 1, normalized size = 0.02 \[ -225 x^{8} - \frac{1860}{7} x^{7} + \frac{581}{3} x^{6} + \frac{1473}{5} x^{5} - 57 x^{4} - \frac{395}{3} x^{3} + 6 x^{2} + 36 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x^8 - 1860/7*x^7 + 581/3*x^6 + 1473/5*x^5 - 57*x^4 - 395/3*x^3 + 6*x^2 + 36
*x

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Sympy [A]  time = 0.088951, size = 44, normalized size = 0.79 \[ - 225 x^{8} - \frac{1860 x^{7}}{7} + \frac{581 x^{6}}{3} + \frac{1473 x^{5}}{5} - 57 x^{4} - \frac{395 x^{3}}{3} + 6 x^{2} + 36 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x**8 - 1860*x**7/7 + 581*x**6/3 + 1473*x**5/5 - 57*x**4 - 395*x**3/3 + 6*x*
*2 + 36*x

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GIAC/XCAS [A]  time = 0.204676, size = 53, normalized size = 0.95 \[ -225 \, x^{8} - \frac{1860}{7} \, x^{7} + \frac{581}{3} \, x^{6} + \frac{1473}{5} \, x^{5} - 57 \, x^{4} - \frac{395}{3} \, x^{3} + 6 \, x^{2} + 36 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x^8 - 1860/7*x^7 + 581/3*x^6 + 1473/5*x^5 - 57*x^4 - 395/3*x^3 + 6*x^2 + 36
*x