Optimal. Leaf size=20 \[ -\frac{15-2 x^2}{10 \sqrt{x^4+5}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0505839, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{15-2 x^2}{10 \sqrt{x^4+5}} \]
Antiderivative was successfully verified.
[In] Int[(x*(2 + 3*x^2))/(5 + x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.2442, size = 17, normalized size = 0.85 \[ - \frac{- 2 x^{2} + 15}{10 \sqrt{x^{4} + 5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(3*x**2+2)/(x**4+5)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0157912, size = 20, normalized size = 1. \[ \frac{2 x^2-15}{10 \sqrt{x^4+5}} \]
Antiderivative was successfully verified.
[In] Integrate[(x*(2 + 3*x^2))/(5 + x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 17, normalized size = 0.9 \[{\frac{2\,{x}^{2}-15}{10}{\frac{1}{\sqrt{{x}^{4}+5}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(3*x^2+2)/(x^4+5)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.776759, size = 30, normalized size = 1.5 \[ \frac{x^{2}}{5 \, \sqrt{x^{4} + 5}} - \frac{3}{2 \, \sqrt{x^{4} + 5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 + 2)*x/(x^4 + 5)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.308302, size = 50, normalized size = 2.5 \[ \frac{3 \, x^{2} - 3 \, \sqrt{x^{4} + 5} + 2}{2 \,{\left (x^{4} - \sqrt{x^{4} + 5} x^{2} + 5\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 + 2)*x/(x^4 + 5)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 13.1521, size = 24, normalized size = 1.2 \[ \frac{x^{2}}{5 \sqrt{x^{4} + 5}} - \frac{3}{2 \sqrt{x^{4} + 5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(3*x**2+2)/(x**4+5)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.270664, size = 22, normalized size = 1.1 \[ \frac{2 \, x^{2} - 15}{10 \, \sqrt{x^{4} + 5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 + 2)*x/(x^4 + 5)^(3/2),x, algorithm="giac")
[Out]