Optimal. Leaf size=54 \[ \frac{a^2 x^4}{4}+\frac{1}{8} x^8 \left (2 a c+b^2\right )+\frac{1}{3} a b x^6+\frac{1}{5} b c x^{10}+\frac{c^2 x^{12}}{12} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.130488, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{a^2 x^4}{4}+\frac{1}{8} x^8 \left (2 a c+b^2\right )+\frac{1}{3} a b x^6+\frac{1}{5} b c x^{10}+\frac{c^2 x^{12}}{12} \]
Antiderivative was successfully verified.
[In] Int[x*(a*x + b*x^3 + c*x^5)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{2} \int ^{x^{2}} x\, dx}{2} + \frac{a b x^{6}}{3} + \frac{b c x^{10}}{5} + \frac{c^{2} x^{12}}{12} + x^{8} \left (\frac{a c}{4} + \frac{b^{2}}{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(c*x**5+b*x**3+a*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0125977, size = 48, normalized size = 0.89 \[ \frac{1}{120} x^4 \left (30 a^2+15 x^4 \left (2 a c+b^2\right )+40 a b x^2+24 b c x^6+10 c^2 x^8\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x*(a*x + b*x^3 + c*x^5)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 45, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{4}}{4}}+{\frac{ab{x}^{6}}{3}}+{\frac{ \left ( 2\,ac+{b}^{2} \right ){x}^{8}}{8}}+{\frac{bc{x}^{10}}{5}}+{\frac{{c}^{2}{x}^{12}}{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(c*x^5+b*x^3+a*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.773449, size = 59, normalized size = 1.09 \[ \frac{1}{12} \, c^{2} x^{12} + \frac{1}{5} \, b c x^{10} + \frac{1}{8} \,{\left (b^{2} + 2 \, a c\right )} x^{8} + \frac{1}{3} \, a b x^{6} + \frac{1}{4} \, a^{2} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^5 + b*x^3 + a*x)^2*x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.247719, size = 1, normalized size = 0.02 \[ \frac{1}{12} x^{12} c^{2} + \frac{1}{5} x^{10} c b + \frac{1}{8} x^{8} b^{2} + \frac{1}{4} x^{8} c a + \frac{1}{3} x^{6} b a + \frac{1}{4} x^{4} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^5 + b*x^3 + a*x)^2*x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.1115, size = 46, normalized size = 0.85 \[ \frac{a^{2} x^{4}}{4} + \frac{a b x^{6}}{3} + \frac{b c x^{10}}{5} + \frac{c^{2} x^{12}}{12} + x^{8} \left (\frac{a c}{4} + \frac{b^{2}}{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(c*x**5+b*x**3+a*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.249277, size = 62, normalized size = 1.15 \[ \frac{1}{12} \, c^{2} x^{12} + \frac{1}{5} \, b c x^{10} + \frac{1}{8} \, b^{2} x^{8} + \frac{1}{4} \, a c x^{8} + \frac{1}{3} \, a b x^{6} + \frac{1}{4} \, a^{2} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^5 + b*x^3 + a*x)^2*x,x, algorithm="giac")
[Out]