Optimal. Leaf size=19 \[ \frac{2}{5} (-x)^{5/2}-\frac{x^2}{2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0111821, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{2}{5} (-x)^{5/2}-\frac{x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[-x]*(Sqrt[-x] + x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.49258, size = 14, normalized size = 0.74 \[ - \frac{x^{2}}{2} + \frac{2 \left (- x\right )^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x)**(1/2)*(x+(-x)**(1/2)),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00753848, size = 19, normalized size = 1. \[ \frac{2}{5} (-x)^{5/2}-\frac{x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[-x]*(Sqrt[-x] + x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 14, normalized size = 0.7 \[{\frac{2}{5} \left ( -x \right ) ^{{\frac{5}{2}}}}-{\frac{{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x)^(1/2)*(x+(-x)^(1/2)),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.717931, size = 18, normalized size = 0.95 \[ \frac{2}{5} \, \left (-x\right )^{\frac{5}{2}} - \frac{1}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x)*(x + sqrt(-x)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.260425, size = 22, normalized size = 1.16 \[ \frac{2}{5} \, \sqrt{-x} x^{2} - \frac{1}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x)*(x + sqrt(-x)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.478577, size = 14, normalized size = 0.74 \[ \frac{2 i x^{\frac{5}{2}}}{5} - \frac{x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x)**(1/2)*(x+(-x)**(1/2)),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.284895, size = 22, normalized size = 1.16 \[ \frac{2}{5} \, \sqrt{-x} x^{2} - \frac{1}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x)*(x + sqrt(-x)),x, algorithm="giac")
[Out]