3.1132 \(\int (1-2 x) (2+3 x)^2 (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{2}{27} (3 x+2)^5+\frac{37}{108} (3 x+2)^4-\frac{7}{81} (3 x+2)^3 \]

[Out]

(-7*(2 + 3*x)^3)/81 + (37*(2 + 3*x)^4)/108 - (2*(2 + 3*x)^5)/27

_______________________________________________________________________________________

Rubi [A]  time = 0.044589, 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 \[ -\frac{2}{27} (3 x+2)^5+\frac{37}{108} (3 x+2)^4-\frac{7}{81} (3 x+2)^3 \]

Antiderivative was successfully verified.

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

[Out]

(-7*(2 + 3*x)^3)/81 + (37*(2 + 3*x)^4)/108 - (2*(2 + 3*x)^5)/27

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 18 x^{5} - \frac{129 x^{4}}{4} - \frac{25 x^{3}}{3} + 12 x + 32 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18*x**5 - 129*x**4/4 - 25*x**3/3 + 12*x + 32*Integral(x, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00138809, size = 28, normalized size = 0.82 \[ -18 x^5-\frac{129 x^4}{4}-\frac{25 x^3}{3}+16 x^2+12 x \]

Antiderivative was successfully verified.

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

[Out]

12*x + 16*x^2 - (25*x^3)/3 - (129*x^4)/4 - 18*x^5

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 25, normalized size = 0.7 \[ -18\,{x}^{5}-{\frac{129\,{x}^{4}}{4}}-{\frac{25\,{x}^{3}}{3}}+16\,{x}^{2}+12\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18*x^5-129/4*x^4-25/3*x^3+16*x^2+12*x

_______________________________________________________________________________________

Maxima [A]  time = 1.35232, size = 32, normalized size = 0.94 \[ -18 \, x^{5} - \frac{129}{4} \, x^{4} - \frac{25}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18*x^5 - 129/4*x^4 - 25/3*x^3 + 16*x^2 + 12*x

_______________________________________________________________________________________

Fricas [A]  time = 0.186526, size = 1, normalized size = 0.03 \[ -18 x^{5} - \frac{129}{4} x^{4} - \frac{25}{3} x^{3} + 16 x^{2} + 12 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18*x^5 - 129/4*x^4 - 25/3*x^3 + 16*x^2 + 12*x

_______________________________________________________________________________________

Sympy [A]  time = 0.075215, size = 26, normalized size = 0.76 \[ - 18 x^{5} - \frac{129 x^{4}}{4} - \frac{25 x^{3}}{3} + 16 x^{2} + 12 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18*x**5 - 129*x**4/4 - 25*x**3/3 + 16*x**2 + 12*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.234392, size = 32, normalized size = 0.94 \[ -18 \, x^{5} - \frac{129}{4} \, x^{4} - \frac{25}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18*x^5 - 129/4*x^4 - 25/3*x^3 + 16*x^2 + 12*x