Optimal. Leaf size=36 \[ \frac{\left (a+b x^3\right )^{4/3}}{4 b^2}-\frac{a \sqrt [3]{a+b x^3}}{b^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0595879, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{\left (a+b x^3\right )^{4/3}}{4 b^2}-\frac{a \sqrt [3]{a+b x^3}}{b^2} \]
Antiderivative was successfully verified.
[In] Int[x^5/(a + b*x^3)^(2/3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.06374, size = 29, normalized size = 0.81 \[ - \frac{a \sqrt [3]{a + b x^{3}}}{b^{2}} + \frac{\left (a + b x^{3}\right )^{\frac{4}{3}}}{4 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(b*x**3+a)**(2/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0197119, size = 27, normalized size = 0.75 \[ \frac{\left (b x^3-3 a\right ) \sqrt [3]{a+b x^3}}{4 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(a + b*x^3)^(2/3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 25, normalized size = 0.7 \[ -{\frac{-b{x}^{3}+3\,a}{4\,{b}^{2}}\sqrt [3]{b{x}^{3}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(b*x^3+a)^(2/3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.42822, size = 41, normalized size = 1.14 \[ \frac{{\left (b x^{3} + a\right )}^{\frac{4}{3}}}{4 \, b^{2}} - \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}} a}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a)^(2/3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.231915, size = 31, normalized size = 0.86 \[ \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}{\left (b x^{3} - 3 \, a\right )}}{4 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a)^(2/3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.71002, size = 44, normalized size = 1.22 \[ \begin{cases} - \frac{3 a \sqrt [3]{a + b x^{3}}}{4 b^{2}} + \frac{x^{3} \sqrt [3]{a + b x^{3}}}{4 b} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{2}{3}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(b*x**3+a)**(2/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.336972, size = 36, normalized size = 1. \[ \frac{{\left (b x^{3} + a\right )}^{\frac{4}{3}} - 4 \,{\left (b x^{3} + a\right )}^{\frac{1}{3}} a}{4 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a)^(2/3),x, algorithm="giac")
[Out]