Optimal. Leaf size=35 \[ \frac{a^3 x^3}{3}+\frac{3}{2} a^2 b x^2+3 a b^2 x+b^3 \log (x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0501241, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{a^3 x^3}{3}+\frac{3}{2} a^2 b x^2+3 a b^2 x+b^3 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3*x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{3} x^{3}}{3} + 3 a^{2} b \int x\, dx + 3 a b^{2} x + b^{3} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3*x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00482502, size = 35, normalized size = 1. \[ \frac{a^3 x^3}{3}+\frac{3}{2} a^2 b x^2+3 a b^2 x+b^3 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3*x^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 32, normalized size = 0.9 \[ 3\,a{b}^{2}x+{\frac{3\,{a}^{2}b{x}^{2}}{2}}+{\frac{{a}^{3}{x}^{3}}{3}}+{b}^{3}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3*x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44423, size = 42, normalized size = 1.2 \[ \frac{1}{3} \, a^{3} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + 3 \, a b^{2} x + b^{3} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.221498, size = 42, normalized size = 1.2 \[ \frac{1}{3} \, a^{3} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + 3 \, a b^{2} x + b^{3} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.07052, size = 34, normalized size = 0.97 \[ \frac{a^{3} x^{3}}{3} + \frac{3 a^{2} b x^{2}}{2} + 3 a b^{2} x + b^{3} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3*x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.226247, size = 43, normalized size = 1.23 \[ \frac{1}{3} \, a^{3} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + 3 \, a b^{2} x + b^{3}{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^2,x, algorithm="giac")
[Out]