3.1147 \(\int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx\)

Optimal. Leaf size=45 \[ -\frac{25}{243} (3 x+2)^6+\frac{13}{27} (3 x+2)^5-\frac{2}{9} (3 x+2)^4+\frac{7}{243} (3 x+2)^3 \]

[Out]

(7*(2 + 3*x)^3)/243 - (2*(2 + 3*x)^4)/9 + (13*(2 + 3*x)^5)/27 - (25*(2 + 3*x)^6)
/243

_______________________________________________________________________________________

Rubi [A]  time = 0.0629512, 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 \[ -\frac{25}{243} (3 x+2)^6+\frac{13}{27} (3 x+2)^5-\frac{2}{9} (3 x+2)^4+\frac{7}{243} (3 x+2)^3 \]

Antiderivative was successfully verified.

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

[Out]

(7*(2 + 3*x)^3)/243 - (2*(2 + 3*x)^4)/9 + (13*(2 + 3*x)^5)/27 - (25*(2 + 3*x)^6)
/243

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 75 x^{6} - 183 x^{5} - 128 x^{4} + \frac{85 x^{3}}{3} + 36 x + 156 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-75*x**6 - 183*x**5 - 128*x**4 + 85*x**3/3 + 36*x + 156*Integral(x, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00171575, size = 31, normalized size = 0.69 \[ -75 x^6-183 x^5-128 x^4+\frac{85 x^3}{3}+78 x^2+36 x \]

Antiderivative was successfully verified.

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

[Out]

36*x + 78*x^2 + (85*x^3)/3 - 128*x^4 - 183*x^5 - 75*x^6

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 30, normalized size = 0.7 \[ -75\,{x}^{6}-183\,{x}^{5}-128\,{x}^{4}+{\frac{85\,{x}^{3}}{3}}+78\,{x}^{2}+36\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-75*x^6-183*x^5-128*x^4+85/3*x^3+78*x^2+36*x

_______________________________________________________________________________________

Maxima [A]  time = 1.34303, size = 39, normalized size = 0.87 \[ -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac{85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-75*x^6 - 183*x^5 - 128*x^4 + 85/3*x^3 + 78*x^2 + 36*x

_______________________________________________________________________________________

Fricas [A]  time = 0.187212, size = 1, normalized size = 0.02 \[ -75 x^{6} - 183 x^{5} - 128 x^{4} + \frac{85}{3} x^{3} + 78 x^{2} + 36 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-75*x^6 - 183*x^5 - 128*x^4 + 85/3*x^3 + 78*x^2 + 36*x

_______________________________________________________________________________________

Sympy [A]  time = 0.080129, size = 29, normalized size = 0.64 \[ - 75 x^{6} - 183 x^{5} - 128 x^{4} + \frac{85 x^{3}}{3} + 78 x^{2} + 36 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-75*x**6 - 183*x**5 - 128*x**4 + 85*x**3/3 + 78*x**2 + 36*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.205801, size = 39, normalized size = 0.87 \[ -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac{85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-75*x^6 - 183*x^5 - 128*x^4 + 85/3*x^3 + 78*x^2 + 36*x