Optimal. Leaf size=20 \[ a x+\frac{b x^3}{3}+\frac{c x^5}{5} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0121312, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a x+\frac{b x^3}{3}+\frac{c x^5}{5} \]
Antiderivative was successfully verified.
[In] Int[a + b*x^2 + c*x^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b x^{3}}{3} + \frac{c x^{5}}{5} + \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(c*x**4+b*x**2+a,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0000787158, size = 20, normalized size = 1. \[ a x+\frac{b x^3}{3}+\frac{c x^5}{5} \]
Antiderivative was successfully verified.
[In] Integrate[a + b*x^2 + c*x^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 17, normalized size = 0.9 \[ ax+{\frac{b{x}^{3}}{3}}+{\frac{c{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(c*x^4+b*x^2+a,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.681658, size = 22, normalized size = 1.1 \[ \frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x^4 + b*x^2 + a,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.233018, size = 1, normalized size = 0.05 \[ \frac{1}{5} x^{5} c + \frac{1}{3} x^{3} b + x a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x^4 + b*x^2 + a,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.054634, size = 15, normalized size = 0.75 \[ a x + \frac{b x^{3}}{3} + \frac{c x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x**4+b*x**2+a,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.261482, size = 22, normalized size = 1.1 \[ \frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x^4 + b*x^2 + a,x, algorithm="giac")
[Out]