Optimal. Leaf size=55 \[ \frac{1}{4} A b^2 x^4+\frac{1}{6} c x^6 (A c+2 b B)+\frac{1}{5} b x^5 (2 A c+b B)+\frac{1}{7} B c^2 x^7 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.128226, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{1}{4} A b^2 x^4+\frac{1}{6} c x^6 (A c+2 b B)+\frac{1}{5} b x^5 (2 A c+b B)+\frac{1}{7} B c^2 x^7 \]
Antiderivative was successfully verified.
[In] Int[x*(A + B*x)*(b*x + c*x^2)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 14.3883, size = 49, normalized size = 0.89 \[ \frac{A b^{2} x^{4}}{4} + \frac{B c^{2} x^{7}}{7} + \frac{b x^{5} \left (2 A c + B b\right )}{5} + \frac{c x^{6} \left (A c + 2 B b\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(B*x+A)*(c*x**2+b*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0137769, size = 55, normalized size = 1. \[ \frac{1}{4} A b^2 x^4+\frac{1}{6} c x^6 (A c+2 b B)+\frac{1}{5} b x^5 (2 A c+b B)+\frac{1}{7} B c^2 x^7 \]
Antiderivative was successfully verified.
[In] Integrate[x*(A + B*x)*(b*x + c*x^2)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 52, normalized size = 1. \[{\frac{B{c}^{2}{x}^{7}}{7}}+{\frac{ \left ( A{c}^{2}+2\,Bbc \right ){x}^{6}}{6}}+{\frac{ \left ( 2\,Abc+{b}^{2}B \right ){x}^{5}}{5}}+{\frac{A{b}^{2}{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(B*x+A)*(c*x^2+b*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.696904, size = 69, normalized size = 1.25 \[ \frac{1}{7} \, B c^{2} x^{7} + \frac{1}{4} \, A b^{2} x^{4} + \frac{1}{6} \,{\left (2 \, B b c + A c^{2}\right )} x^{6} + \frac{1}{5} \,{\left (B b^{2} + 2 \, A b c\right )} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)*x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.250336, size = 1, normalized size = 0.02 \[ \frac{1}{7} x^{7} c^{2} B + \frac{1}{3} x^{6} c b B + \frac{1}{6} x^{6} c^{2} A + \frac{1}{5} x^{5} b^{2} B + \frac{2}{5} x^{5} c b A + \frac{1}{4} x^{4} b^{2} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)*x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.124604, size = 54, normalized size = 0.98 \[ \frac{A b^{2} x^{4}}{4} + \frac{B c^{2} x^{7}}{7} + x^{6} \left (\frac{A c^{2}}{6} + \frac{B b c}{3}\right ) + x^{5} \left (\frac{2 A b c}{5} + \frac{B b^{2}}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(B*x+A)*(c*x**2+b*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.26672, size = 72, normalized size = 1.31 \[ \frac{1}{7} \, B c^{2} x^{7} + \frac{1}{3} \, B b c x^{6} + \frac{1}{6} \, A c^{2} x^{6} + \frac{1}{5} \, B b^{2} x^{5} + \frac{2}{5} \, A b c x^{5} + \frac{1}{4} \, A b^{2} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)*x,x, algorithm="giac")
[Out]