Optimal. Leaf size=48 \[ \frac{4 b \sqrt{a x+b x^4}}{9 a^2 x^2}-\frac{2 \sqrt{a x+b x^4}}{9 a x^5} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.117729, antiderivative size = 48, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{4 b \sqrt{a x+b x^4}}{9 a^2 x^2}-\frac{2 \sqrt{a x+b x^4}}{9 a x^5} \]
Antiderivative was successfully verified.
[In] Int[1/(x^5*Sqrt[a*x + b*x^4]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 12.2708, size = 42, normalized size = 0.88 \[ - \frac{2 \sqrt{a x + b x^{4}}}{9 a x^{5}} + \frac{4 b \sqrt{a x + b x^{4}}}{9 a^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**5/(b*x**4+a*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0349873, size = 31, normalized size = 0.65 \[ -\frac{2 \left (a-2 b x^3\right ) \sqrt{x \left (a+b x^3\right )}}{9 a^2 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^5*Sqrt[a*x + b*x^4]),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 35, normalized size = 0.7 \[ -{\frac{ \left ( 2\,b{x}^{3}+2\,a \right ) \left ( -2\,b{x}^{3}+a \right ) }{9\,{a}^{2}{x}^{4}}{\frac{1}{\sqrt{b{x}^{4}+ax}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^5/(b*x^4+a*x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41109, size = 51, normalized size = 1.06 \[ \frac{2 \,{\left (2 \, b^{2} x^{7} + a b x^{4} - a^{2} x\right )}}{9 \, \sqrt{b x^{3} + a} a^{2} x^{\frac{11}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a*x)*x^5),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215991, size = 39, normalized size = 0.81 \[ \frac{2 \, \sqrt{b x^{4} + a x}{\left (2 \, b x^{3} - a\right )}}{9 \, a^{2} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a*x)*x^5),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{x^{5} \sqrt{x \left (a + b x^{3}\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**5/(b*x**4+a*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.223347, size = 36, normalized size = 0.75 \[ -\frac{2 \,{\left ({\left (b + \frac{a}{x^{3}}\right )}^{\frac{3}{2}} - 3 \, \sqrt{b + \frac{a}{x^{3}}} b\right )}}{9 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a*x)*x^5),x, algorithm="giac")
[Out]