Optimal. Leaf size=42 \[ \frac{B \left (b+c x^2\right )^4}{8 c^2}-\frac{\left (b+c x^2\right )^3 (b B-A c)}{6 c^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.172439, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{B \left (b+c x^2\right )^4}{8 c^2}-\frac{\left (b+c x^2\right )^3 (b B-A c)}{6 c^2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 16.4412, size = 34, normalized size = 0.81 \[ \frac{B \left (b + c x^{2}\right )^{4}}{8 c^{2}} + \frac{\left (b + c x^{2}\right )^{3} \left (A c - B b\right )}{6 c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x**2+A)*(c*x**4+b*x**2)**2/x**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0227073, size = 51, normalized size = 1.21 \[ \frac{1}{24} x^2 \left (12 A b^2+4 c x^4 (A c+2 b B)+6 b x^2 (2 A c+b B)+3 B c^2 x^6\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 52, normalized size = 1.2 \[{\frac{B{c}^{2}{x}^{8}}{8}}+{\frac{ \left ( A{c}^{2}+2\,Bbc \right ){x}^{6}}{6}}+{\frac{ \left ( 2\,Abc+{b}^{2}B \right ){x}^{4}}{4}}+{\frac{A{x}^{2}{b}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x^2+A)*(c*x^4+b*x^2)^2/x^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.37941, size = 69, normalized size = 1.64 \[ \frac{1}{8} \, B c^{2} x^{8} + \frac{1}{6} \,{\left (2 \, B b c + A c^{2}\right )} x^{6} + \frac{1}{2} \, A b^{2} x^{2} + \frac{1}{4} \,{\left (B b^{2} + 2 \, A b c\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2*(B*x^2 + A)/x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.221945, size = 69, normalized size = 1.64 \[ \frac{1}{8} \, B c^{2} x^{8} + \frac{1}{6} \,{\left (2 \, B b c + A c^{2}\right )} x^{6} + \frac{1}{2} \, A b^{2} x^{2} + \frac{1}{4} \,{\left (B b^{2} + 2 \, A b c\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2*(B*x^2 + A)/x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.059048, size = 53, normalized size = 1.26 \[ \frac{A b^{2} x^{2}}{2} + \frac{B c^{2} x^{8}}{8} + x^{6} \left (\frac{A c^{2}}{6} + \frac{B b c}{3}\right ) + x^{4} \left (\frac{A b c}{2} + \frac{B b^{2}}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x**2+A)*(c*x**4+b*x**2)**2/x**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.207763, size = 72, normalized size = 1.71 \[ \frac{1}{8} \, B c^{2} x^{8} + \frac{1}{3} \, B b c x^{6} + \frac{1}{6} \, A c^{2} x^{6} + \frac{1}{4} \, B b^{2} x^{4} + \frac{1}{2} \, A b c x^{4} + \frac{1}{2} \, A b^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2*(B*x^2 + A)/x^3,x, algorithm="giac")
[Out]