Optimal. Leaf size=19 \[ -\frac{\left (b+c x^2\right )^4}{8 b x^8} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0228797, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{\left (b+c x^2\right )^4}{8 b x^8} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2 + c*x^4)^3/x^15,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.16102, size = 15, normalized size = 0.79 \[ - \frac{\left (b + c x^{2}\right )^{4}}{8 b x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2)**3/x**15,x)
[Out]
_______________________________________________________________________________________
Mathematica [B] time = 0.0113402, size = 43, normalized size = 2.26 \[ -\frac{b^3}{8 x^8}-\frac{b^2 c}{2 x^6}-\frac{3 b c^2}{4 x^4}-\frac{c^3}{2 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2 + c*x^4)^3/x^15,x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.007, size = 36, normalized size = 1.9 \[ -{\frac{{b}^{3}}{8\,{x}^{8}}}-{\frac{{b}^{2}c}{2\,{x}^{6}}}-{\frac{{c}^{3}}{2\,{x}^{2}}}-{\frac{3\,b{c}^{2}}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2)^3/x^15,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.695561, size = 47, normalized size = 2.47 \[ -\frac{4 \, c^{3} x^{6} + 6 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} + b^{3}}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3/x^15,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.246106, size = 47, normalized size = 2.47 \[ -\frac{4 \, c^{3} x^{6} + 6 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} + b^{3}}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3/x^15,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.63611, size = 37, normalized size = 1.95 \[ - \frac{b^{3} + 4 b^{2} c x^{2} + 6 b c^{2} x^{4} + 4 c^{3} x^{6}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2)**3/x**15,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.268212, size = 47, normalized size = 2.47 \[ -\frac{4 \, c^{3} x^{6} + 6 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} + b^{3}}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3/x^15,x, algorithm="giac")
[Out]