3.1328 \(\int (1-2 x)^3 (2+3 x) (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{5}{16} (1-2 x)^6+\frac{17}{10} (1-2 x)^5-\frac{77}{32} (1-2 x)^4 \]

[Out]

(-77*(1 - 2*x)^4)/32 + (17*(1 - 2*x)^5)/10 - (5*(1 - 2*x)^6)/16

_______________________________________________________________________________________

Rubi [A]  time = 0.0469735, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{5}{16} (1-2 x)^6+\frac{17}{10} (1-2 x)^5-\frac{77}{32} (1-2 x)^4 \]

Antiderivative was successfully verified.

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

[Out]

(-77*(1 - 2*x)^4)/32 + (17*(1 - 2*x)^5)/10 - (5*(1 - 2*x)^6)/16

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 20 x^{6} + \frac{28 x^{5}}{5} + \frac{45 x^{4}}{2} - 9 x^{3} + 6 x - 17 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20*x**6 + 28*x**5/5 + 45*x**4/2 - 9*x**3 + 6*x - 17*Integral(x, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00128505, size = 35, normalized size = 1.03 \[ -20 x^6+\frac{28 x^5}{5}+\frac{45 x^4}{2}-9 x^3-\frac{17 x^2}{2}+6 x \]

Antiderivative was successfully verified.

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

[Out]

6*x - (17*x^2)/2 - 9*x^3 + (45*x^4)/2 + (28*x^5)/5 - 20*x^6

_______________________________________________________________________________________

Maple [A]  time = 0., size = 30, normalized size = 0.9 \[ -20\,{x}^{6}+{\frac{28\,{x}^{5}}{5}}+{\frac{45\,{x}^{4}}{2}}-9\,{x}^{3}-{\frac{17\,{x}^{2}}{2}}+6\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20*x^6+28/5*x^5+45/2*x^4-9*x^3-17/2*x^2+6*x

_______________________________________________________________________________________

Maxima [A]  time = 1.3485, size = 39, normalized size = 1.15 \[ -20 \, x^{6} + \frac{28}{5} \, x^{5} + \frac{45}{2} \, x^{4} - 9 \, x^{3} - \frac{17}{2} \, x^{2} + 6 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20*x^6 + 28/5*x^5 + 45/2*x^4 - 9*x^3 - 17/2*x^2 + 6*x

_______________________________________________________________________________________

Fricas [A]  time = 0.186382, size = 1, normalized size = 0.03 \[ -20 x^{6} + \frac{28}{5} x^{5} + \frac{45}{2} x^{4} - 9 x^{3} - \frac{17}{2} x^{2} + 6 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20*x^6 + 28/5*x^5 + 45/2*x^4 - 9*x^3 - 17/2*x^2 + 6*x

_______________________________________________________________________________________

Sympy [A]  time = 0.078336, size = 32, normalized size = 0.94 \[ - 20 x^{6} + \frac{28 x^{5}}{5} + \frac{45 x^{4}}{2} - 9 x^{3} - \frac{17 x^{2}}{2} + 6 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20*x**6 + 28*x**5/5 + 45*x**4/2 - 9*x**3 - 17*x**2/2 + 6*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.208441, size = 39, normalized size = 1.15 \[ -20 \, x^{6} + \frac{28}{5} \, x^{5} + \frac{45}{2} \, x^{4} - 9 \, x^{3} - \frac{17}{2} \, x^{2} + 6 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20*x^6 + 28/5*x^5 + 45/2*x^4 - 9*x^3 - 17/2*x^2 + 6*x