Optimal. Leaf size=23 \[ -\frac{2}{5} x \sqrt{x^5+1} \sqrt{\frac{a}{x^7}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0156065, antiderivative size = 23, 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 \[ -\frac{2}{5} x \sqrt{x^5+1} \sqrt{\frac{a}{x^7}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a/x^7]/Sqrt[1 + x^5],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.01607, size = 22, normalized size = 0.96 \[ - \frac{2 x \sqrt{\frac{a}{x^{7}}} \sqrt{x^{5} + 1}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a/x**7)**(1/2)/(x**5+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0160049, size = 23, normalized size = 1. \[ -\frac{2}{5} x \sqrt{x^5+1} \sqrt{\frac{a}{x^7}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a/x^7]/Sqrt[1 + x^5],x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.008, size = 37, normalized size = 1.6 \[ -{\frac{2\,x \left ( 1+x \right ) \left ({x}^{4}-{x}^{3}+{x}^{2}-x+1 \right ) }{5}\sqrt{{\frac{a}{{x}^{7}}}}{\frac{1}{\sqrt{{x}^{5}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a/x^7)^(1/2)/(x^5+1)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.779543, size = 55, normalized size = 2.39 \[ -\frac{2 \,{\left (\sqrt{a} x^{6} + \sqrt{a} x\right )}}{5 \, \sqrt{x^{4} - x^{3} + x^{2} - x + 1} \sqrt{x + 1} x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a/x^7)/sqrt(x^5 + 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.286137, size = 23, normalized size = 1. \[ -\frac{2}{5} \, \sqrt{x^{5} + 1} x \sqrt{\frac{a}{x^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a/x^7)/sqrt(x^5 + 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{\frac{a}{x^{7}}}}{\sqrt{\left (x + 1\right ) \left (x^{4} - x^{3} + x^{2} - x + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a/x**7)**(1/2)/(x**5+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.274373, size = 38, normalized size = 1.65 \[ -\frac{2 \, a^{3}{\left (\frac{\sqrt{a + \frac{a}{x^{5}}}}{a^{2}} - \frac{1}{a^{\frac{3}{2}}}\right )}}{5 \,{\left | a \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a/x^7)/sqrt(x^5 + 1),x, algorithm="giac")
[Out]