Optimal. Leaf size=59 \[ \frac{2 a^2 \sqrt{a+b x^3}}{3 b^3}+\frac{2 \left (a+b x^3\right )^{5/2}}{15 b^3}-\frac{4 a \left (a+b x^3\right )^{3/2}}{9 b^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0878251, 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 \[ \frac{2 a^2 \sqrt{a+b x^3}}{3 b^3}+\frac{2 \left (a+b x^3\right )^{5/2}}{15 b^3}-\frac{4 a \left (a+b x^3\right )^{3/2}}{9 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^8/Sqrt[a + b*x^3],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.8279, size = 54, normalized size = 0.92 \[ \frac{2 a^{2} \sqrt{a + b x^{3}}}{3 b^{3}} - \frac{4 a \left (a + b x^{3}\right )^{\frac{3}{2}}}{9 b^{3}} + \frac{2 \left (a + b x^{3}\right )^{\frac{5}{2}}}{15 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8/(b*x**3+a)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0264136, size = 39, normalized size = 0.66 \[ \frac{2 \sqrt{a+b x^3} \left (8 a^2-4 a b x^3+3 b^2 x^6\right )}{45 b^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^8/Sqrt[a + b*x^3],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 36, normalized size = 0.6 \[{\frac{6\,{b}^{2}{x}^{6}-8\,ab{x}^{3}+16\,{a}^{2}}{45\,{b}^{3}}\sqrt{b{x}^{3}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8/(b*x^3+a)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43605, size = 63, normalized size = 1.07 \[ \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{5}{2}}}{15 \, b^{3}} - \frac{4 \,{\left (b x^{3} + a\right )}^{\frac{3}{2}} a}{9 \, b^{3}} + \frac{2 \, \sqrt{b x^{3} + a} a^{2}}{3 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(b*x^3 + a),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.223603, size = 47, normalized size = 0.8 \[ \frac{2 \,{\left (3 \, b^{2} x^{6} - 4 \, a b x^{3} + 8 \, a^{2}\right )} \sqrt{b x^{3} + a}}{45 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(b*x^3 + a),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.84583, size = 70, normalized size = 1.19 \[ \begin{cases} \frac{16 a^{2} \sqrt{a + b x^{3}}}{45 b^{3}} - \frac{8 a x^{3} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15 b} & \text{for}\: b \neq 0 \\\frac{x^{9}}{9 \sqrt{a}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8/(b*x**3+a)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.225241, size = 58, normalized size = 0.98 \[ \frac{2 \,{\left (3 \,{\left (b x^{3} + a\right )}^{\frac{5}{2}} - 10 \,{\left (b x^{3} + a\right )}^{\frac{3}{2}} a + 15 \, \sqrt{b x^{3} + a} a^{2}\right )}}{45 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(b*x^3 + a),x, algorithm="giac")
[Out]