3.1146 \(\int (1-2 x) (2+3 x)^3 (3+5 x)^2 \, dx\)

Optimal. Leaf size=45 \[ -\frac{50}{567} (3 x+2)^7+\frac{65}{162} (3 x+2)^6-\frac{8}{45} (3 x+2)^5+\frac{7}{324} (3 x+2)^4 \]

[Out]

(7*(2 + 3*x)^4)/324 - (8*(2 + 3*x)^5)/45 + (65*(2 + 3*x)^6)/162 - (50*(2 + 3*x)^
7)/567

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Rubi [A]  time = 0.0642145, 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 \[ -\frac{50}{567} (3 x+2)^7+\frac{65}{162} (3 x+2)^6-\frac{8}{45} (3 x+2)^5+\frac{7}{324} (3 x+2)^4 \]

Antiderivative was successfully verified.

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

[Out]

(7*(2 + 3*x)^4)/324 - (8*(2 + 3*x)^5)/45 + (65*(2 + 3*x)^6)/162 - (50*(2 + 3*x)^
7)/567

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{1350 x^{7}}{7} - \frac{1215 x^{6}}{2} - \frac{3366 x^{5}}{5} - \frac{769 x^{4}}{4} + \frac{638 x^{3}}{3} + 72 x + 420 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350*x**7/7 - 1215*x**6/2 - 3366*x**5/5 - 769*x**4/4 + 638*x**3/3 + 72*x + 420*
Integral(x, x)

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Mathematica [A]  time = 0.00160407, size = 44, normalized size = 0.98 \[ -\frac{1350 x^7}{7}-\frac{1215 x^6}{2}-\frac{3366 x^5}{5}-\frac{769 x^4}{4}+\frac{638 x^3}{3}+210 x^2+72 x \]

Antiderivative was successfully verified.

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

[Out]

72*x + 210*x^2 + (638*x^3)/3 - (769*x^4)/4 - (3366*x^5)/5 - (1215*x^6)/2 - (1350
*x^7)/7

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Maple [A]  time = 0.001, size = 35, normalized size = 0.8 \[ -{\frac{1350\,{x}^{7}}{7}}-{\frac{1215\,{x}^{6}}{2}}-{\frac{3366\,{x}^{5}}{5}}-{\frac{769\,{x}^{4}}{4}}+{\frac{638\,{x}^{3}}{3}}+210\,{x}^{2}+72\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350/7*x^7-1215/2*x^6-3366/5*x^5-769/4*x^4+638/3*x^3+210*x^2+72*x

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Maxima [A]  time = 1.34734, size = 46, normalized size = 1.02 \[ -\frac{1350}{7} \, x^{7} - \frac{1215}{2} \, x^{6} - \frac{3366}{5} \, x^{5} - \frac{769}{4} \, x^{4} + \frac{638}{3} \, x^{3} + 210 \, x^{2} + 72 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350/7*x^7 - 1215/2*x^6 - 3366/5*x^5 - 769/4*x^4 + 638/3*x^3 + 210*x^2 + 72*x

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Fricas [A]  time = 0.18112, size = 1, normalized size = 0.02 \[ -\frac{1350}{7} x^{7} - \frac{1215}{2} x^{6} - \frac{3366}{5} x^{5} - \frac{769}{4} x^{4} + \frac{638}{3} x^{3} + 210 x^{2} + 72 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350/7*x^7 - 1215/2*x^6 - 3366/5*x^5 - 769/4*x^4 + 638/3*x^3 + 210*x^2 + 72*x

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Sympy [A]  time = 0.087396, size = 41, normalized size = 0.91 \[ - \frac{1350 x^{7}}{7} - \frac{1215 x^{6}}{2} - \frac{3366 x^{5}}{5} - \frac{769 x^{4}}{4} + \frac{638 x^{3}}{3} + 210 x^{2} + 72 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350*x**7/7 - 1215*x**6/2 - 3366*x**5/5 - 769*x**4/4 + 638*x**3/3 + 210*x**2 +
72*x

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GIAC/XCAS [A]  time = 0.207986, size = 46, normalized size = 1.02 \[ -\frac{1350}{7} \, x^{7} - \frac{1215}{2} \, x^{6} - \frac{3366}{5} \, x^{5} - \frac{769}{4} \, x^{4} + \frac{638}{3} \, x^{3} + 210 \, x^{2} + 72 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350/7*x^7 - 1215/2*x^6 - 3366/5*x^5 - 769/4*x^4 + 638/3*x^3 + 210*x^2 + 72*x