Optimal. Leaf size=20 \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0146872, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[(a*x^2 + b*x^3 + c*x^4)/x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ b \int x\, dx + \frac{c x^{3}}{3} + \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**3+a*x**2)/x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00161879, size = 20, normalized size = 1. \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x^2 + b*x^3 + c*x^4)/x^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 17, normalized size = 0.9 \[ ax+{\frac{b{x}^{2}}{2}}+{\frac{c{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^3+a*x^2)/x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.749836, size = 22, normalized size = 1.1 \[ \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^3 + a*x^2)/x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.254699, size = 22, normalized size = 1.1 \[ \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^3 + a*x^2)/x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.067583, size = 15, normalized size = 0.75 \[ a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**3+a*x**2)/x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.263675, size = 22, normalized size = 1.1 \[ \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^3 + a*x^2)/x^2,x, algorithm="giac")
[Out]