3.138 \(\int (-3+2 x) \left (-3 x+x^2\right )^{2/3} \, dx\)

Optimal. Leaf size=15 \[ \frac{3}{5} \left (x^2-3 x\right )^{5/3} \]

[Out]

(3*(-3*x + x^2)^(5/3))/5

_______________________________________________________________________________________

Rubi [A]  time = 0.00849011, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{3}{5} \left (x^2-3 x\right )^{5/3} \]

Antiderivative was successfully verified.

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

[Out]

(3*(-3*x + x^2)^(5/3))/5

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.59438, size = 12, normalized size = 0.8 \[ \frac{3 \left (x^{2} - 3 x\right )^{\frac{5}{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*(x**2 - 3*x)**(5/3)/5

_______________________________________________________________________________________

Mathematica [A]  time = 0.0165649, size = 13, normalized size = 0.87 \[ \frac{3}{5} ((x-3) x)^{5/3} \]

Antiderivative was successfully verified.

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

[Out]

(3*((-3 + x)*x)^(5/3))/5

_______________________________________________________________________________________

Maple [A]  time = 0.005, size = 16, normalized size = 1.1 \[{\frac{ \left ( -9+3\,x \right ) x}{5} \left ({x}^{2}-3\,x \right ) ^{{\frac{2}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-3+2*x)*(x^2-3*x)^(2/3),x)

[Out]

3/5*(-3+x)*x*(x^2-3*x)^(2/3)

_______________________________________________________________________________________

Maxima [A]  time = 0.715396, size = 15, normalized size = 1. \[ \frac{3}{5} \,{\left (x^{2} - 3 \, x\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/5*(x^2 - 3*x)^(5/3)

_______________________________________________________________________________________

Fricas [A]  time = 0.27612, size = 15, normalized size = 1. \[ \frac{3}{5} \,{\left (x^{2} - 3 \, x\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/5*(x^2 - 3*x)^(5/3)

_______________________________________________________________________________________

Sympy [A]  time = 0.406947, size = 31, normalized size = 2.07 \[ \frac{3 x^{2} \left (x^{2} - 3 x\right )^{\frac{2}{3}}}{5} - \frac{9 x \left (x^{2} - 3 x\right )^{\frac{2}{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*x**2*(x**2 - 3*x)**(2/3)/5 - 9*x*(x**2 - 3*x)**(2/3)/5

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.270857, size = 15, normalized size = 1. \[ \frac{3}{5} \,{\left (x^{2} - 3 \, x\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/5*(x^2 - 3*x)^(5/3)