Optimal. Leaf size=43 \[ -\frac{a^3}{21 x^{21}}-\frac{a^2 b}{6 x^{18}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0503132, antiderivative size = 43, 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 \[ -\frac{a^3}{21 x^{21}}-\frac{a^2 b}{6 x^{18}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^3/x^22,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 8.77914, size = 37, normalized size = 0.86 \[ - \frac{a^{3}}{21 x^{21}} - \frac{a^{2} b}{6 x^{18}} - \frac{a b^{2}}{5 x^{15}} - \frac{b^{3}}{12 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3/x**22,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00678364, size = 43, normalized size = 1. \[ -\frac{a^3}{21 x^{21}}-\frac{a^2 b}{6 x^{18}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^3/x^22,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{21\,{x}^{21}}}-{\frac{{a}^{2}b}{6\,{x}^{18}}}-{\frac{a{b}^{2}}{5\,{x}^{15}}}-{\frac{{b}^{3}}{12\,{x}^{12}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3/x^22,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.46574, size = 50, normalized size = 1.16 \[ -\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^22,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.203003, size = 50, normalized size = 1.16 \[ -\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^22,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.30862, size = 39, normalized size = 0.91 \[ - \frac{20 a^{3} + 70 a^{2} b x^{3} + 84 a b^{2} x^{6} + 35 b^{3} x^{9}}{420 x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3/x**22,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.215303, size = 50, normalized size = 1.16 \[ -\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^22,x, algorithm="giac")
[Out]