Optimal. Leaf size=59 \[ \frac{a^2 \left (a+b x^3\right )^{2/3}}{2 b^3}+\frac{\left (a+b x^3\right )^{8/3}}{8 b^3}-\frac{2 a \left (a+b x^3\right )^{5/3}}{5 b^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0845142, antiderivative size = 59, 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 \[ \frac{a^2 \left (a+b x^3\right )^{2/3}}{2 b^3}+\frac{\left (a+b x^3\right )^{8/3}}{8 b^3}-\frac{2 a \left (a+b x^3\right )^{5/3}}{5 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^8/(a + b*x^3)^(1/3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.648, size = 51, normalized size = 0.86 \[ \frac{a^{2} \left (a + b x^{3}\right )^{\frac{2}{3}}}{2 b^{3}} - \frac{2 a \left (a + b x^{3}\right )^{\frac{5}{3}}}{5 b^{3}} + \frac{\left (a + b x^{3}\right )^{\frac{8}{3}}}{8 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8/(b*x**3+a)**(1/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0278168, size = 39, normalized size = 0.66 \[ \frac{\left (a+b x^3\right )^{2/3} \left (9 a^2-6 a b x^3+5 b^2 x^6\right )}{40 b^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^8/(a + b*x^3)^(1/3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 36, normalized size = 0.6 \[{\frac{5\,{b}^{2}{x}^{6}-6\,ab{x}^{3}+9\,{a}^{2}}{40\,{b}^{3}} \left ( b{x}^{3}+a \right ) ^{{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8/(b*x^3+a)^(1/3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.4293, size = 63, normalized size = 1.07 \[ \frac{{\left (b x^{3} + a\right )}^{\frac{8}{3}}}{8 \, b^{3}} - \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{5}{3}} a}{5 \, b^{3}} + \frac{{\left (b x^{3} + a\right )}^{\frac{2}{3}} a^{2}}{2 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(b*x^3 + a)^(1/3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.24973, size = 47, normalized size = 0.8 \[ \frac{{\left (5 \, b^{2} x^{6} - 6 \, a b x^{3} + 9 \, a^{2}\right )}{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{40 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(b*x^3 + a)^(1/3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.75244, size = 68, normalized size = 1.15 \[ \begin{cases} \frac{9 a^{2} \left (a + b x^{3}\right )^{\frac{2}{3}}}{40 b^{3}} - \frac{3 a x^{3} \left (a + b x^{3}\right )^{\frac{2}{3}}}{20 b^{2}} + \frac{x^{6} \left (a + b x^{3}\right )^{\frac{2}{3}}}{8 b} & \text{for}\: b \neq 0 \\\frac{x^{9}}{9 \sqrt [3]{a}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8/(b*x**3+a)**(1/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.307921, size = 58, normalized size = 0.98 \[ \frac{5 \,{\left (b x^{3} + a\right )}^{\frac{8}{3}} - 16 \,{\left (b x^{3} + a\right )}^{\frac{5}{3}} a + 20 \,{\left (b x^{3} + a\right )}^{\frac{2}{3}} a^{2}}{40 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(b*x^3 + a)^(1/3),x, algorithm="giac")
[Out]