Optimal. Leaf size=25 \[ \frac{2 \sqrt{x^3+1} \sqrt{a x^4}}{3 x^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00999083, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{2 \sqrt{x^3+1} \sqrt{a x^4}}{3 x^2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a*x^4]/Sqrt[1 + x^3],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.52583, size = 22, normalized size = 0.88 \[ \frac{2 \sqrt{a x^{4}} \sqrt{x^{3} + 1}}{3 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a*x**4)**(1/2)/(x**3+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0087445, size = 25, normalized size = 1. \[ \frac{2 \sqrt{x^3+1} \sqrt{a x^4}}{3 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a*x^4]/Sqrt[1 + x^3],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 31, normalized size = 1.2 \[{\frac{ \left ( 2+2\,x \right ) \left ({x}^{2}-x+1 \right ) }{3\,{x}^{2}}\sqrt{a{x}^{4}}{\frac{1}{\sqrt{{x}^{3}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a*x^4)^(1/2)/(x^3+1)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.794808, size = 38, normalized size = 1.52 \[ \frac{2 \,{\left (\sqrt{a} x^{3} + \sqrt{a}\right )}}{3 \, \sqrt{x^{2} - x + 1} \sqrt{x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a*x^4)/sqrt(x^3 + 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.274466, size = 26, normalized size = 1.04 \[ \frac{2 \, \sqrt{a x^{4}} \sqrt{x^{3} + 1}}{3 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a*x^4)/sqrt(x^3 + 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{a x^{4}}}{\sqrt{\left (x + 1\right ) \left (x^{2} - x + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x**4)**(1/2)/(x**3+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.26073, size = 16, normalized size = 0.64 \[ \frac{2}{3} \, \sqrt{x^{3} + 1} \sqrt{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a*x^4)/sqrt(x^3 + 1),x, algorithm="giac")
[Out]