3.2 \(\int \left (a x^3+b x^6\right )^{2/3} \, dx\)

Optimal. Leaf size=25 \[ \frac{\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \]

[Out]

(a*x^3 + b*x^6)^(5/3)/(5*b*x^5)

_______________________________________________________________________________________

Rubi [A]  time = 0.0126025, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \]

Antiderivative was successfully verified.

[In]  Int[(a*x^3 + b*x^6)^(2/3),x]

[Out]

(a*x^3 + b*x^6)^(5/3)/(5*b*x^5)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 1.37952, size = 19, normalized size = 0.76 \[ \frac{\left (a x^{3} + b x^{6}\right )^{\frac{5}{3}}}{5 b x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**6+a*x**3)**(2/3),x)

[Out]

(a*x**3 + b*x**6)**(5/3)/(5*b*x**5)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0160823, size = 25, normalized size = 1. \[ \frac{\left (x^3 \left (a+b x^3\right )\right )^{5/3}}{5 b x^5} \]

Antiderivative was successfully verified.

[In]  Integrate[(a*x^3 + b*x^6)^(2/3),x]

[Out]

(x^3*(a + b*x^3))^(5/3)/(5*b*x^5)

_______________________________________________________________________________________

Maple [A]  time = 0.006, size = 29, normalized size = 1.2 \[{\frac{b{x}^{3}+a}{5\,b{x}^{2}} \left ( b{x}^{6}+a{x}^{3} \right ) ^{{\frac{2}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^6+a*x^3)^(2/3),x)

[Out]

1/5*(b*x^3+a)/b/x^2*(b*x^6+a*x^3)^(2/3)

_______________________________________________________________________________________

Maxima [A]  time = 0.771503, size = 19, normalized size = 0.76 \[ \frac{{\left (b x^{3} + a\right )}^{\frac{5}{3}}}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^6 + a*x^3)^(2/3),x, algorithm="maxima")

[Out]

1/5*(b*x^3 + a)^(5/3)/b

_______________________________________________________________________________________

Fricas [A]  time = 0.263995, size = 38, normalized size = 1.52 \[ \frac{{\left (b x^{6} + a x^{3}\right )}^{\frac{2}{3}}{\left (b x^{3} + a\right )}}{5 \, b x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^6 + a*x^3)^(2/3),x, algorithm="fricas")

[Out]

1/5*(b*x^6 + a*x^3)^(2/3)*(b*x^3 + a)/(b*x^2)

_______________________________________________________________________________________

Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \left (a x^{3} + b x^{6}\right )^{\frac{2}{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**6+a*x**3)**(2/3),x)

[Out]

Integral((a*x**3 + b*x**6)**(2/3), x)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.285731, size = 19, normalized size = 0.76 \[ \frac{{\left (b x^{3} + a\right )}^{\frac{5}{3}}}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^6 + a*x^3)^(2/3),x, algorithm="giac")

[Out]

1/5*(b*x^3 + a)^(5/3)/b