Optimal. Leaf size=67 \[ -\frac{a^5}{9 x^9}-\frac{5 a^4 b}{8 x^8}-\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0519505, antiderivative size = 67, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a^5}{9 x^9}-\frac{5 a^4 b}{8 x^8}-\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^5/x^10,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.5387, size = 65, normalized size = 0.97 \[ - \frac{a^{5}}{9 x^{9}} - \frac{5 a^{4} b}{8 x^{8}} - \frac{10 a^{3} b^{2}}{7 x^{7}} - \frac{5 a^{2} b^{3}}{3 x^{6}} - \frac{a b^{4}}{x^{5}} - \frac{b^{5}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5/x**10,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00928879, size = 67, normalized size = 1. \[ -\frac{a^5}{9 x^9}-\frac{5 a^4 b}{8 x^8}-\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^5/x^10,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 58, normalized size = 0.9 \[ -{\frac{{a}^{5}}{9\,{x}^{9}}}-{\frac{5\,{a}^{4}b}{8\,{x}^{8}}}-{\frac{10\,{a}^{3}{b}^{2}}{7\,{x}^{7}}}-{\frac{5\,{a}^{2}{b}^{3}}{3\,{x}^{6}}}-{\frac{a{b}^{4}}{{x}^{5}}}-{\frac{{b}^{5}}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5/x^10,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33215, size = 77, normalized size = 1.15 \[ -\frac{126 \, b^{5} x^{5} + 504 \, a b^{4} x^{4} + 840 \, a^{2} b^{3} x^{3} + 720 \, a^{3} b^{2} x^{2} + 315 \, a^{4} b x + 56 \, a^{5}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^10,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.191349, size = 77, normalized size = 1.15 \[ -\frac{126 \, b^{5} x^{5} + 504 \, a b^{4} x^{4} + 840 \, a^{2} b^{3} x^{3} + 720 \, a^{3} b^{2} x^{2} + 315 \, a^{4} b x + 56 \, a^{5}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^10,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.20348, size = 61, normalized size = 0.91 \[ - \frac{56 a^{5} + 315 a^{4} b x + 720 a^{3} b^{2} x^{2} + 840 a^{2} b^{3} x^{3} + 504 a b^{4} x^{4} + 126 b^{5} x^{5}}{504 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5/x**10,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.213393, size = 77, normalized size = 1.15 \[ -\frac{126 \, b^{5} x^{5} + 504 \, a b^{4} x^{4} + 840 \, a^{2} b^{3} x^{3} + 720 \, a^{3} b^{2} x^{2} + 315 \, a^{4} b x + 56 \, a^{5}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^10,x, algorithm="giac")
[Out]