Optimal. Leaf size=12 \[ c x+\frac{d x^2}{2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0191222, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.037 \[ c x+\frac{d x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(a*c + (b*c + a*d)*x + b*d*x^2)/(a + b*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ d \int x\, dx + \int c\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a*c+(a*d+b*c)*x+b*d*x**2)/(b*x+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00153336, size = 12, normalized size = 1. \[ c x+\frac{d x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a*c + (b*c + a*d)*x + b*d*x^2)/(a + b*x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 11, normalized size = 0.9 \[ cx+{\frac{d{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a*c+(a*d+b*c)*x+x^2*b*d)/(b*x+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.730066, size = 14, normalized size = 1.17 \[ \frac{1}{2} \, d x^{2} + c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*d*x^2 + a*c + (b*c + a*d)*x)/(b*x + a),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.194038, size = 14, normalized size = 1.17 \[ \frac{1}{2} \, d x^{2} + c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*d*x^2 + a*c + (b*c + a*d)*x)/(b*x + a),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.111742, size = 8, normalized size = 0.67 \[ c x + \frac{d x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*c+(a*d+b*c)*x+b*d*x**2)/(b*x+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.208054, size = 14, normalized size = 1.17 \[ \frac{1}{2} \, d x^{2} + c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*d*x^2 + a*c + (b*c + a*d)*x)/(b*x + a),x, algorithm="giac")
[Out]