Optimal. Leaf size=8 \[ \tan ^{-1}\left (2 \sqrt{x}\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0102897, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \tan ^{-1}\left (2 \sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[(Sqrt[x] + 4*x^(3/2))^(-1),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.32601, size = 7, normalized size = 0.88 \[ \operatorname{atan}{\left (2 \sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(4*x**(3/2)+x**(1/2)),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00550019, size = 8, normalized size = 1. \[ \tan ^{-1}\left (2 \sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(Sqrt[x] + 4*x^(3/2))^(-1),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 7, normalized size = 0.9 \[ \arctan \left ( 2\,\sqrt{x} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(4*x^(3/2)+x^(1/2)),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.796948, size = 8, normalized size = 1. \[ \arctan \left (2 \, \sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(4*x^(3/2) + sqrt(x)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.271161, size = 8, normalized size = 1. \[ \arctan \left (2 \, \sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(4*x^(3/2) + sqrt(x)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.555798, size = 7, normalized size = 0.88 \[ \operatorname{atan}{\left (2 \sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(4*x**(3/2)+x**(1/2)),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.277453, size = 8, normalized size = 1. \[ \arctan \left (2 \, \sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(4*x^(3/2) + sqrt(x)),x, algorithm="giac")
[Out]