Optimal. Leaf size=19 \[ -\frac{1}{2 b^2 x \sqrt{b x^2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00884721, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{1}{2 b^2 x \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[x^2/(b*x^2)^(5/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.37507, size = 17, normalized size = 0.89 \[ - \frac{\sqrt{b x^{2}}}{2 b^{3} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(b*x**2)**(5/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00283697, size = 16, normalized size = 0.84 \[ -\frac{x^3}{2 \left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(b*x^2)^(5/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 13, normalized size = 0.7 \[ -{\frac{{x}^{3}}{2} \left ( b{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(b*x^2)^(5/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43291, size = 11, normalized size = 0.58 \[ -\frac{1}{2 \, b^{\frac{5}{2}} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^2)^(5/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.216139, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{b x^{2}}}{2 \, b^{3} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^2)^(5/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.0454, size = 17, normalized size = 0.89 \[ - \frac{x^{3}}{2 b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(b*x**2)**(5/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.527038, size = 4, normalized size = 0.21 \[ \mathit{sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^2)^(5/2),x, algorithm="giac")
[Out]