3.1327 \(\int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx\)

Optimal. Leaf size=45 \[ \frac{45}{112} (1-2 x)^7-\frac{103}{32} (1-2 x)^6+\frac{707}{80} (1-2 x)^5-\frac{539}{64} (1-2 x)^4 \]

[Out]

(-539*(1 - 2*x)^4)/64 + (707*(1 - 2*x)^5)/80 - (103*(1 - 2*x)^6)/32 + (45*(1 - 2
*x)^7)/112

_______________________________________________________________________________________

Rubi [A]  time = 0.0629023, 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 \[ \frac{45}{112} (1-2 x)^7-\frac{103}{32} (1-2 x)^6+\frac{707}{80} (1-2 x)^5-\frac{539}{64} (1-2 x)^4 \]

Antiderivative was successfully verified.

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

[Out]

(-539*(1 - 2*x)^4)/64 + (707*(1 - 2*x)^5)/80 - (103*(1 - 2*x)^6)/32 + (45*(1 - 2
*x)^7)/112

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{360 x^{7}}{7} - 26 x^{6} + \frac{326 x^{5}}{5} + \frac{99 x^{4}}{4} - 35 x^{3} + 12 x - 16 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-360*x**7/7 - 26*x**6 + 326*x**5/5 + 99*x**4/4 - 35*x**3 + 12*x - 16*Integral(x,
x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00188534, size = 40, normalized size = 0.89 \[ -\frac{360 x^7}{7}-26 x^6+\frac{326 x^5}{5}+\frac{99 x^4}{4}-35 x^3-8 x^2+12 x \]

Antiderivative was successfully verified.

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

[Out]

12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 35, normalized size = 0.8 \[ -{\frac{360\,{x}^{7}}{7}}-26\,{x}^{6}+{\frac{326\,{x}^{5}}{5}}+{\frac{99\,{x}^{4}}{4}}-35\,{x}^{3}-8\,{x}^{2}+12\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-360/7*x^7-26*x^6+326/5*x^5+99/4*x^4-35*x^3-8*x^2+12*x

_______________________________________________________________________________________

Maxima [A]  time = 1.33941, size = 46, normalized size = 1.02 \[ -\frac{360}{7} \, x^{7} - 26 \, x^{6} + \frac{326}{5} \, x^{5} + \frac{99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x

_______________________________________________________________________________________

Fricas [A]  time = 0.184522, size = 1, normalized size = 0.02 \[ -\frac{360}{7} x^{7} - 26 x^{6} + \frac{326}{5} x^{5} + \frac{99}{4} x^{4} - 35 x^{3} - 8 x^{2} + 12 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x

_______________________________________________________________________________________

Sympy [A]  time = 0.084587, size = 37, normalized size = 0.82 \[ - \frac{360 x^{7}}{7} - 26 x^{6} + \frac{326 x^{5}}{5} + \frac{99 x^{4}}{4} - 35 x^{3} - 8 x^{2} + 12 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-360*x**7/7 - 26*x**6 + 326*x**5/5 + 99*x**4/4 - 35*x**3 - 8*x**2 + 12*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.207672, size = 46, normalized size = 1.02 \[ -\frac{360}{7} \, x^{7} - 26 \, x^{6} + \frac{326}{5} \, x^{5} + \frac{99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x