Optimal. Leaf size=54 \[ \frac{a^2 x^3}{3}+\frac{1}{5} x^5 \left (2 a c+b^2\right )+\frac{1}{2} a b x^4+\frac{1}{3} b c x^6+\frac{c^2 x^7}{7} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0606733, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a^2 x^3}{3}+\frac{1}{5} x^5 \left (2 a c+b^2\right )+\frac{1}{2} a b x^4+\frac{1}{3} b c x^6+\frac{c^2 x^7}{7} \]
Antiderivative was successfully verified.
[In] Int[(a*x^2 + b*x^3 + c*x^4)^2/x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 13.1869, size = 48, normalized size = 0.89 \[ \frac{a^{2} x^{3}}{3} + \frac{a b x^{4}}{2} + \frac{b c x^{6}}{3} + \frac{c^{2} x^{7}}{7} + x^{5} \left (\frac{2 a c}{5} + \frac{b^{2}}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**3+a*x**2)**2/x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0101182, size = 54, normalized size = 1. \[ \frac{a^2 x^3}{3}+\frac{1}{5} x^5 \left (2 a c+b^2\right )+\frac{1}{2} a b x^4+\frac{1}{3} b c x^6+\frac{c^2 x^7}{7} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x^2 + b*x^3 + c*x^4)^2/x^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 45, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{3}}{3}}+{\frac{ab{x}^{4}}{2}}+{\frac{ \left ( 2\,ac+{b}^{2} \right ){x}^{5}}{5}}+{\frac{bc{x}^{6}}{3}}+{\frac{{c}^{2}{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^3+a*x^2)^2/x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.752253, size = 59, normalized size = 1.09 \[ \frac{1}{7} \, c^{2} x^{7} + \frac{1}{3} \, b c x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{5} \,{\left (b^{2} + 2 \, a c\right )} x^{5} + \frac{1}{3} \, a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^3 + a*x^2)^2/x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.267614, size = 59, normalized size = 1.09 \[ \frac{1}{7} \, c^{2} x^{7} + \frac{1}{3} \, b c x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{5} \,{\left (b^{2} + 2 \, a c\right )} x^{5} + \frac{1}{3} \, a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^3 + a*x^2)^2/x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.107811, size = 48, normalized size = 0.89 \[ \frac{a^{2} x^{3}}{3} + \frac{a b x^{4}}{2} + \frac{b c x^{6}}{3} + \frac{c^{2} x^{7}}{7} + x^{5} \left (\frac{2 a c}{5} + \frac{b^{2}}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**3+a*x**2)**2/x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.260175, size = 62, normalized size = 1.15 \[ \frac{1}{7} \, c^{2} x^{7} + \frac{1}{3} \, b c x^{6} + \frac{1}{5} \, b^{2} x^{5} + \frac{2}{5} \, a c x^{5} + \frac{1}{2} \, a b x^{4} + \frac{1}{3} \, a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^3 + a*x^2)^2/x^2,x, algorithm="giac")
[Out]