Optimal. Leaf size=38 \[ -\frac{A b-a B}{5 b^2 (a+b x)^5}-\frac{B}{4 b^2 (a+b x)^4} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0553206, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ -\frac{A b-a B}{5 b^2 (a+b x)^5}-\frac{B}{4 b^2 (a+b x)^4} \]
Antiderivative was successfully verified.
[In] Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 18.6347, size = 32, normalized size = 0.84 \[ - \frac{B}{4 b^{2} \left (a + b x\right )^{4}} - \frac{A b - B a}{5 b^{2} \left (a + b x\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0186675, size = 27, normalized size = 0.71 \[ -\frac{B (a+5 b x)+4 A b}{20 b^2 (a+b x)^5} \]
Antiderivative was successfully verified.
[In] Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 35, normalized size = 0.9 \[ -{\frac{Ab-Ba}{5\,{b}^{2} \left ( bx+a \right ) ^{5}}}-{\frac{B}{4\,{b}^{2} \left ( bx+a \right ) ^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)/(b^2*x^2+2*a*b*x+a^2)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.679854, size = 97, normalized size = 2.55 \[ -\frac{5 \, B b x + B a + 4 \, A b}{20 \,{\left (b^{7} x^{5} + 5 \, a b^{6} x^{4} + 10 \, a^{2} b^{5} x^{3} + 10 \, a^{3} b^{4} x^{2} + 5 \, a^{4} b^{3} x + a^{5} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)/(b^2*x^2 + 2*a*b*x + a^2)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.257385, size = 97, normalized size = 2.55 \[ -\frac{5 \, B b x + B a + 4 \, A b}{20 \,{\left (b^{7} x^{5} + 5 \, a b^{6} x^{4} + 10 \, a^{2} b^{5} x^{3} + 10 \, a^{3} b^{4} x^{2} + 5 \, a^{4} b^{3} x + a^{5} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)/(b^2*x^2 + 2*a*b*x + a^2)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.73942, size = 76, normalized size = 2. \[ - \frac{4 A b + B a + 5 B b x}{20 a^{5} b^{2} + 100 a^{4} b^{3} x + 200 a^{3} b^{4} x^{2} + 200 a^{2} b^{5} x^{3} + 100 a b^{6} x^{4} + 20 b^{7} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.270793, size = 34, normalized size = 0.89 \[ -\frac{5 \, B b x + B a + 4 \, A b}{20 \,{\left (b x + a\right )}^{5} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)/(b^2*x^2 + 2*a*b*x + a^2)^3,x, algorithm="giac")
[Out]