Optimal. Leaf size=15 \[ -\frac{b^2}{d^3 (a+b x)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0113412, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{b^2}{d^3 (a+b x)} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/((a*d)/b + d*x)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.26964, size = 12, normalized size = 0.8 \[ - \frac{b^{2}}{d^{3} \left (a + b x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/(a*d/b+d*x)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00598944, size = 15, normalized size = 1. \[ -\frac{b^2}{d^3 (a+b x)} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/((a*d)/b + d*x)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0., size = 16, normalized size = 1.1 \[ -{\frac{{b}^{2}}{{d}^{3} \left ( bx+a \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/(a*d/b+d*x)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34255, size = 26, normalized size = 1.73 \[ -\frac{b^{2}}{b d^{3} x + a d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(d*x + a*d/b)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.198634, size = 26, normalized size = 1.73 \[ -\frac{b^{2}}{b d^{3} x + a d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(d*x + a*d/b)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.24688, size = 19, normalized size = 1.27 \[ - \frac{b^{3}}{a b d^{3} + b^{2} d^{3} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/(a*d/b+d*x)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.210464, size = 20, normalized size = 1.33 \[ -\frac{b^{2}}{{\left (b x + a\right )} d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(d*x + a*d/b)^3,x, algorithm="giac")
[Out]