Optimal. Leaf size=24 \[ a^2 \log (x)-\frac{a b}{x^2}-\frac{b^2}{4 x^4} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0498924, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ a^2 \log (x)-\frac{a b}{x^2}-\frac{b^2}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^2/x,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 8.15532, size = 24, normalized size = 1. \[ \frac{a^{2} \log{\left (x^{2} \right )}}{2} - \frac{a b}{x^{2}} - \frac{b^{2}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**2/x,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00146136, size = 24, normalized size = 1. \[ a^2 \log (x)-\frac{a b}{x^2}-\frac{b^2}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^2/x,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 23, normalized size = 1. \[ -{\frac{{b}^{2}}{4\,{x}^{4}}}-{\frac{ab}{{x}^{2}}}+{a}^{2}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^2/x,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43841, size = 35, normalized size = 1.46 \[ \frac{1}{2} \, a^{2} \log \left (x^{2}\right ) - \frac{4 \, a b x^{2} + b^{2}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.228801, size = 38, normalized size = 1.58 \[ \frac{4 \, a^{2} x^{4} \log \left (x\right ) - 4 \, a b x^{2} - b^{2}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.28235, size = 22, normalized size = 0.92 \[ a^{2} \log{\left (x \right )} - \frac{4 a b x^{2} + b^{2}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**2/x,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.234907, size = 46, normalized size = 1.92 \[ \frac{1}{2} \, a^{2}{\rm ln}\left (x^{2}\right ) - \frac{3 \, a^{2} x^{4} + 4 \, a b x^{2} + b^{2}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x,x, algorithm="giac")
[Out]