3.1260 \(\int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{500 (3 x+2)^9}{6561}-\frac{475}{729} (3 x+2)^8+\frac{8285 (3 x+2)^7}{5103}-\frac{4099 (3 x+2)^6}{4374}+\frac{763 (3 x+2)^5}{3645}-\frac{49 (3 x+2)^4}{2916} \]

[Out]

(-49*(2 + 3*x)^4)/2916 + (763*(2 + 3*x)^5)/3645 - (4099*(2 + 3*x)^6)/4374 + (828
5*(2 + 3*x)^7)/5103 - (475*(2 + 3*x)^8)/729 + (500*(2 + 3*x)^9)/6561

_______________________________________________________________________________________

Rubi [A]  time = 0.0956704, antiderivative size = 67, 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 \[ \frac{500 (3 x+2)^9}{6561}-\frac{475}{729} (3 x+2)^8+\frac{8285 (3 x+2)^7}{5103}-\frac{4099 (3 x+2)^6}{4374}+\frac{763 (3 x+2)^5}{3645}-\frac{49 (3 x+2)^4}{2916} \]

Antiderivative was successfully verified.

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

[Out]

(-49*(2 + 3*x)^4)/2916 + (763*(2 + 3*x)^5)/3645 - (4099*(2 + 3*x)^6)/4374 + (828
5*(2 + 3*x)^7)/5103 - (475*(2 + 3*x)^8)/729 + (500*(2 + 3*x)^9)/6561

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ 1500 x^{9} + 4725 x^{8} + \frac{33255 x^{7}}{7} + \frac{121 x^{6}}{6} - \frac{15709 x^{5}}{5} - \frac{7145 x^{4}}{4} + 258 x^{3} + 216 x + 1188 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500*x**9 + 4725*x**8 + 33255*x**7/7 + 121*x**6/6 - 15709*x**5/5 - 7145*x**4/4 +
258*x**3 + 216*x + 1188*Integral(x, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0040721, size = 52, normalized size = 0.78 \[ 1500 x^9+4725 x^8+\frac{33255 x^7}{7}+\frac{121 x^6}{6}-\frac{15709 x^5}{5}-\frac{7145 x^4}{4}+258 x^3+594 x^2+216 x \]

Antiderivative was successfully verified.

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

[Out]

216*x + 594*x^2 + 258*x^3 - (7145*x^4)/4 - (15709*x^5)/5 + (121*x^6)/6 + (33255*
x^7)/7 + 4725*x^8 + 1500*x^9

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 45, normalized size = 0.7 \[ 1500\,{x}^{9}+4725\,{x}^{8}+{\frac{33255\,{x}^{7}}{7}}+{\frac{121\,{x}^{6}}{6}}-{\frac{15709\,{x}^{5}}{5}}-{\frac{7145\,{x}^{4}}{4}}+258\,{x}^{3}+594\,{x}^{2}+216\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500*x^9+4725*x^8+33255/7*x^7+121/6*x^6-15709/5*x^5-7145/4*x^4+258*x^3+594*x^2+2
16*x

_______________________________________________________________________________________

Maxima [A]  time = 1.35002, size = 59, normalized size = 0.88 \[ 1500 \, x^{9} + 4725 \, x^{8} + \frac{33255}{7} \, x^{7} + \frac{121}{6} \, x^{6} - \frac{15709}{5} \, x^{5} - \frac{7145}{4} \, x^{4} + 258 \, x^{3} + 594 \, x^{2} + 216 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500*x^9 + 4725*x^8 + 33255/7*x^7 + 121/6*x^6 - 15709/5*x^5 - 7145/4*x^4 + 258*x
^3 + 594*x^2 + 216*x

_______________________________________________________________________________________

Fricas [A]  time = 0.177569, size = 1, normalized size = 0.01 \[ 1500 x^{9} + 4725 x^{8} + \frac{33255}{7} x^{7} + \frac{121}{6} x^{6} - \frac{15709}{5} x^{5} - \frac{7145}{4} x^{4} + 258 x^{3} + 594 x^{2} + 216 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500*x^9 + 4725*x^8 + 33255/7*x^7 + 121/6*x^6 - 15709/5*x^5 - 7145/4*x^4 + 258*x
^3 + 594*x^2 + 216*x

_______________________________________________________________________________________

Sympy [A]  time = 0.105592, size = 49, normalized size = 0.73 \[ 1500 x^{9} + 4725 x^{8} + \frac{33255 x^{7}}{7} + \frac{121 x^{6}}{6} - \frac{15709 x^{5}}{5} - \frac{7145 x^{4}}{4} + 258 x^{3} + 594 x^{2} + 216 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500*x**9 + 4725*x**8 + 33255*x**7/7 + 121*x**6/6 - 15709*x**5/5 - 7145*x**4/4 +
258*x**3 + 594*x**2 + 216*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.220386, size = 59, normalized size = 0.88 \[ 1500 \, x^{9} + 4725 \, x^{8} + \frac{33255}{7} \, x^{7} + \frac{121}{6} \, x^{6} - \frac{15709}{5} \, x^{5} - \frac{7145}{4} \, x^{4} + 258 \, x^{3} + 594 \, x^{2} + 216 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500*x^9 + 4725*x^8 + 33255/7*x^7 + 121/6*x^6 - 15709/5*x^5 - 7145/4*x^4 + 258*x
^3 + 594*x^2 + 216*x