Optimal. Leaf size=36 \[ -\frac{\left (a+b x^3\right )^{5/3} \, _2F_1\left (1,\frac{4}{3};\frac{2}{3};-\frac{b x^3}{a}\right )}{a x} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0515646, antiderivative size = 49, normalized size of antiderivative = 1.36, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{\left (a+b x^3\right )^{2/3} \, _2F_1\left (-\frac{2}{3},-\frac{1}{3};\frac{2}{3};-\frac{b x^3}{a}\right )}{x \left (\frac{b x^3}{a}+1\right )^{2/3}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^(2/3)/x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.86368, size = 42, normalized size = 1.17 \[ - \frac{\left (a + b x^{3}\right )^{\frac{2}{3}}{{}_{2}F_{1}\left (\begin{matrix} - \frac{2}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle |{- \frac{b x^{3}}{a}} \right )}}{x \left (1 + \frac{b x^{3}}{a}\right )^{\frac{2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**(2/3)/x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0358899, size = 63, normalized size = 1.75 \[ \frac{b x^3 \sqrt [3]{\frac{b x^3}{a}+1} \, _2F_1\left (\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right )-a-b x^3}{x \sqrt [3]{a+b x^3}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^(2/3)/x^2,x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.038, size = 0, normalized size = 0. \[ \int{\frac{1}{{x}^{2}} \left ( b{x}^{3}+a \right ) ^{{\frac{2}{3}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^(2/3)/x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)/x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{x^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)/x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.52361, size = 41, normalized size = 1.14 \[ \frac{a^{\frac{2}{3}} \Gamma \left (- \frac{1}{3}\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{2}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle |{\frac{b x^{3} e^{i \pi }}{a}} \right )}}{3 x \Gamma \left (\frac{2}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**(2/3)/x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)/x^2,x, algorithm="giac")
[Out]