Optimal. Leaf size=65 \[ -\frac{a^5}{x}+\frac{5}{2} a^4 b x^2+2 a^3 b^2 x^5+\frac{5}{4} a^2 b^3 x^8+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{14}}{14} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0585079, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a^5}{x}+\frac{5}{2} a^4 b x^2+2 a^3 b^2 x^5+\frac{5}{4} a^2 b^3 x^8+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{14}}{14} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^5/x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{5}}{x} + 5 a^{4} b \int x\, dx + 2 a^{3} b^{2} x^{5} + \frac{5 a^{2} b^{3} x^{8}}{4} + \frac{5 a b^{4} x^{11}}{11} + \frac{b^{5} x^{14}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5/x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00713306, size = 65, normalized size = 1. \[ -\frac{a^5}{x}+\frac{5}{2} a^4 b x^2+2 a^3 b^2 x^5+\frac{5}{4} a^2 b^3 x^8+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{14}}{14} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^5/x^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 58, normalized size = 0.9 \[ -{\frac{{a}^{5}}{x}}+{\frac{5\,{a}^{4}b{x}^{2}}{2}}+2\,{a}^{3}{b}^{2}{x}^{5}+{\frac{5\,{a}^{2}{b}^{3}{x}^{8}}{4}}+{\frac{5\,a{b}^{4}{x}^{11}}{11}}+{\frac{{b}^{5}{x}^{14}}{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5/x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43463, size = 77, normalized size = 1.18 \[ \frac{1}{14} \, b^{5} x^{14} + \frac{5}{11} \, a b^{4} x^{11} + \frac{5}{4} \, a^{2} b^{3} x^{8} + 2 \, a^{3} b^{2} x^{5} + \frac{5}{2} \, a^{4} b x^{2} - \frac{a^{5}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.205099, size = 80, normalized size = 1.23 \[ \frac{22 \, b^{5} x^{15} + 140 \, a b^{4} x^{12} + 385 \, a^{2} b^{3} x^{9} + 616 \, a^{3} b^{2} x^{6} + 770 \, a^{4} b x^{3} - 308 \, a^{5}}{308 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.17163, size = 61, normalized size = 0.94 \[ - \frac{a^{5}}{x} + \frac{5 a^{4} b x^{2}}{2} + 2 a^{3} b^{2} x^{5} + \frac{5 a^{2} b^{3} x^{8}}{4} + \frac{5 a b^{4} x^{11}}{11} + \frac{b^{5} x^{14}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5/x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.226459, size = 77, normalized size = 1.18 \[ \frac{1}{14} \, b^{5} x^{14} + \frac{5}{11} \, a b^{4} x^{11} + \frac{5}{4} \, a^{2} b^{3} x^{8} + 2 \, a^{3} b^{2} x^{5} + \frac{5}{2} \, a^{4} b x^{2} - \frac{a^{5}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^2,x, algorithm="giac")
[Out]