Optimal. Leaf size=16 \[ -\frac{1}{7 \left (a+b x+c x^2\right )^7} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00910288, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ -\frac{1}{7 \left (a+b x+c x^2\right )^7} \]
Antiderivative was successfully verified.
[In] Int[(b + 2*c*x)/(a + b*x + c*x^2)^8,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.66627, size = 15, normalized size = 0.94 \[ - \frac{1}{7 \left (a + b x + c x^{2}\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*c*x+b)/(c*x**2+b*x+a)**8,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0177459, size = 15, normalized size = 0.94 \[ -\frac{1}{7 (a+x (b+c x))^7} \]
Antiderivative was successfully verified.
[In] Integrate[(b + 2*c*x)/(a + b*x + c*x^2)^8,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 15, normalized size = 0.9 \[ -{\frac{1}{7\, \left ( c{x}^{2}+bx+a \right ) ^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*c*x+b)/(c*x^2+b*x+a)^8,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.763245, size = 19, normalized size = 1.19 \[ -\frac{1}{7 \,{\left (c x^{2} + b x + a\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/(c*x^2 + b*x + a)^8,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.327656, size = 473, normalized size = 29.56 \[ -\frac{1}{7 \,{\left (c^{7} x^{14} + 7 \, b c^{6} x^{13} + 7 \,{\left (3 \, b^{2} c^{5} + a c^{6}\right )} x^{12} + 7 \,{\left (5 \, b^{3} c^{4} + 6 \, a b c^{5}\right )} x^{11} + 7 \,{\left (5 \, b^{4} c^{3} + 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right )} x^{10} + 7 \,{\left (3 \, b^{5} c^{2} + 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right )} x^{9} + 7 \,{\left (b^{6} c + 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 5 \, a^{3} c^{4}\right )} x^{8} + 7 \, a^{6} b x +{\left (b^{7} + 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} + 140 \, a^{3} b c^{3}\right )} x^{7} + a^{7} + 7 \,{\left (a b^{6} + 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 5 \, a^{4} c^{3}\right )} x^{6} + 7 \,{\left (3 \, a^{2} b^{5} + 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right )} x^{5} + 7 \,{\left (5 \, a^{3} b^{4} + 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right )} x^{4} + 7 \,{\left (5 \, a^{4} b^{3} + 6 \, a^{5} b c\right )} x^{3} + 7 \,{\left (3 \, a^{5} b^{2} + a^{6} c\right )} x^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/(c*x^2 + b*x + a)^8,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x+b)/(c*x**2+b*x+a)**8,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.274759, size = 19, normalized size = 1.19 \[ -\frac{1}{7 \,{\left (c x^{2} + b x + a\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/(c*x^2 + b*x + a)^8,x, algorithm="giac")
[Out]