Optimal. Leaf size=43 \[ -\frac{b^3}{9 x^9}-\frac{3 b^2 c}{7 x^7}-\frac{3 b c^2}{5 x^5}-\frac{c^3}{3 x^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0454872, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{b^3}{9 x^9}-\frac{3 b^2 c}{7 x^7}-\frac{3 b c^2}{5 x^5}-\frac{c^3}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2 + c*x^4)^3/x^16,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.89588, size = 41, normalized size = 0.95 \[ - \frac{b^{3}}{9 x^{9}} - \frac{3 b^{2} c}{7 x^{7}} - \frac{3 b c^{2}}{5 x^{5}} - \frac{c^{3}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2)**3/x**16,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00667005, size = 43, normalized size = 1. \[ -\frac{b^3}{9 x^9}-\frac{3 b^2 c}{7 x^7}-\frac{3 b c^2}{5 x^5}-\frac{c^3}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2 + c*x^4)^3/x^16,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 36, normalized size = 0.8 \[ -{\frac{{b}^{3}}{9\,{x}^{9}}}-{\frac{3\,{b}^{2}c}{7\,{x}^{7}}}-{\frac{3\,b{c}^{2}}{5\,{x}^{5}}}-{\frac{{c}^{3}}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2)^3/x^16,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.692134, size = 50, normalized size = 1.16 \[ -\frac{105 \, c^{3} x^{6} + 189 \, b c^{2} x^{4} + 135 \, b^{2} c x^{2} + 35 \, b^{3}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3/x^16,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.249166, size = 50, normalized size = 1.16 \[ -\frac{105 \, c^{3} x^{6} + 189 \, b c^{2} x^{4} + 135 \, b^{2} c x^{2} + 35 \, b^{3}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3/x^16,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.66973, size = 39, normalized size = 0.91 \[ - \frac{35 b^{3} + 135 b^{2} c x^{2} + 189 b c^{2} x^{4} + 105 c^{3} x^{6}}{315 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2)**3/x**16,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.268588, size = 50, normalized size = 1.16 \[ -\frac{105 \, c^{3} x^{6} + 189 \, b c^{2} x^{4} + 135 \, b^{2} c x^{2} + 35 \, b^{3}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3/x^16,x, algorithm="giac")
[Out]