Optimal. Leaf size=33 \[ -\frac{a B+A b}{4 x^4}-\frac{a A}{5 x^5}-\frac{b B}{3 x^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0419066, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ -\frac{a B+A b}{4 x^4}-\frac{a A}{5 x^5}-\frac{b B}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(A + B*x))/x^6,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.58898, size = 31, normalized size = 0.94 \[ - \frac{A a}{5 x^{5}} - \frac{B b}{3 x^{3}} - \frac{\frac{A b}{4} + \frac{B a}{4}}{x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(B*x+A)/x**6,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0155947, size = 31, normalized size = 0.94 \[ -\frac{3 a (4 A+5 B x)+5 b x (3 A+4 B x)}{60 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(A + B*x))/x^6,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 28, normalized size = 0.9 \[ -{\frac{Aa}{5\,{x}^{5}}}-{\frac{Bb}{3\,{x}^{3}}}-{\frac{Ab+Ba}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(B*x+A)/x^6,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35656, size = 36, normalized size = 1.09 \[ -\frac{20 \, B b x^{2} + 12 \, A a + 15 \,{\left (B a + A b\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^6,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.194647, size = 36, normalized size = 1.09 \[ -\frac{20 \, B b x^{2} + 12 \, A a + 15 \,{\left (B a + A b\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^6,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.32656, size = 31, normalized size = 0.94 \[ - \frac{12 A a + 20 B b x^{2} + x \left (15 A b + 15 B a\right )}{60 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(B*x+A)/x**6,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.27023, size = 36, normalized size = 1.09 \[ -\frac{20 \, B b x^{2} + 15 \, B a x + 15 \, A b x + 12 \, A a}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^6,x, algorithm="giac")
[Out]