Optimal. Leaf size=75 \[ \frac{1}{3} A b^3 x^3+\frac{1}{4} b^2 x^4 (3 A c+b B)+\frac{1}{6} c^2 x^6 (A c+3 b B)+\frac{3}{5} b c x^5 (A c+b B)+\frac{1}{7} B c^3 x^7 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.133166, antiderivative size = 75, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{1}{3} A b^3 x^3+\frac{1}{4} b^2 x^4 (3 A c+b B)+\frac{1}{6} c^2 x^6 (A c+3 b B)+\frac{3}{5} b c x^5 (A c+b B)+\frac{1}{7} B c^3 x^7 \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2)^3)/x,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 17.0415, size = 70, normalized size = 0.93 \[ \frac{A b^{3} x^{3}}{3} + \frac{B c^{3} x^{7}}{7} + \frac{b^{2} x^{4} \left (3 A c + B b\right )}{4} + \frac{3 b c x^{5} \left (A c + B b\right )}{5} + \frac{c^{2} x^{6} \left (A c + 3 B b\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)**3/x,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0172868, size = 75, normalized size = 1. \[ \frac{1}{3} A b^3 x^3+\frac{1}{4} b^2 x^4 (3 A c+b B)+\frac{1}{6} c^2 x^6 (A c+3 b B)+\frac{3}{5} b c x^5 (A c+b B)+\frac{1}{7} B c^3 x^7 \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2)^3)/x,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 76, normalized size = 1. \[{\frac{B{c}^{3}{x}^{7}}{7}}+{\frac{ \left ( A{c}^{3}+3\,Bb{c}^{2} \right ){x}^{6}}{6}}+{\frac{ \left ( 3\,Ab{c}^{2}+3\,B{b}^{2}c \right ){x}^{5}}{5}}+{\frac{ \left ( 3\,A{b}^{2}c+B{b}^{3} \right ){x}^{4}}{4}}+{\frac{A{b}^{3}{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)^3/x,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.69628, size = 99, normalized size = 1.32 \[ \frac{1}{7} \, B c^{3} x^{7} + \frac{1}{3} \, A b^{3} x^{3} + \frac{1}{6} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{6} + \frac{3}{5} \,{\left (B b^{2} c + A b c^{2}\right )} x^{5} + \frac{1}{4} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.259035, size = 99, normalized size = 1.32 \[ \frac{1}{7} \, B c^{3} x^{7} + \frac{1}{3} \, A b^{3} x^{3} + \frac{1}{6} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{6} + \frac{3}{5} \,{\left (B b^{2} c + A b c^{2}\right )} x^{5} + \frac{1}{4} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.144958, size = 82, normalized size = 1.09 \[ \frac{A b^{3} x^{3}}{3} + \frac{B c^{3} x^{7}}{7} + x^{6} \left (\frac{A c^{3}}{6} + \frac{B b c^{2}}{2}\right ) + x^{5} \left (\frac{3 A b c^{2}}{5} + \frac{3 B b^{2} c}{5}\right ) + x^{4} \left (\frac{3 A b^{2} c}{4} + \frac{B b^{3}}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)**3/x,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.268146, size = 104, normalized size = 1.39 \[ \frac{1}{7} \, B c^{3} x^{7} + \frac{1}{2} \, B b c^{2} x^{6} + \frac{1}{6} \, A c^{3} x^{6} + \frac{3}{5} \, B b^{2} c x^{5} + \frac{3}{5} \, A b c^{2} x^{5} + \frac{1}{4} \, B b^{3} x^{4} + \frac{3}{4} \, A b^{2} c x^{4} + \frac{1}{3} \, A b^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x,x, algorithm="giac")
[Out]