Optimal. Leaf size=12 \[ c x+\frac{d x^2}{2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0165543, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.033 \[ c x+\frac{d x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3),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((b*d*x**4+b*c*x**3+a*d*x+a*c)/(b*x**3+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00143704, size = 12, normalized size = 1. \[ c x+\frac{d x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3),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((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.40989, 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^4 + b*c*x^3 + a*d*x + a*c)/(b*x^3 + a),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.216175, 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^4 + b*c*x^3 + a*d*x + a*c)/(b*x^3 + a),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.059286, 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((b*d*x**4+b*c*x**3+a*d*x+a*c)/(b*x**3+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.216064, 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^4 + b*c*x^3 + a*d*x + a*c)/(b*x^3 + a),x, algorithm="giac")
[Out]