3.21 \(\int x^{3/2} \, dx\)

Optimal. Leaf size=9 \[ \frac{2 x^{5/2}}{5} \]

[Out]

(2*x^(5/2))/5

_______________________________________________________________________________________

Rubi [A]  time = 0.00301936, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{2 x^{5/2}}{5} \]

Antiderivative was successfully verified.

[In]  Int[x^(3/2),x]

[Out]

(2*x^(5/2))/5

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 0.902529, size = 7, normalized size = 0.78 \[ \frac{2 x^{\frac{5}{2}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**(3/2),x)

[Out]

2*x**(5/2)/5

_______________________________________________________________________________________

Mathematica [A]  time = 0.00094139, size = 9, normalized size = 1. \[ \frac{2 x^{5/2}}{5} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(3/2),x]

[Out]

(2*x^(5/2))/5

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 6, normalized size = 0.7 \[{\frac{2}{5}{x}^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^(3/2),x)

[Out]

2/5*x^(5/2)

_______________________________________________________________________________________

Maxima [A]  time = 1.32588, size = 7, normalized size = 0.78 \[ \frac{2}{5} \, x^{\frac{5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(3/2),x, algorithm="maxima")

[Out]

2/5*x^(5/2)

_______________________________________________________________________________________

Fricas [A]  time = 0.200177, size = 7, normalized size = 0.78 \[ \frac{2}{5} \, x^{\frac{5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(3/2),x, algorithm="fricas")

[Out]

2/5*x^(5/2)

_______________________________________________________________________________________

Sympy [A]  time = 0.02991, size = 7, normalized size = 0.78 \[ \frac{2 x^{\frac{5}{2}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**(3/2),x)

[Out]

2*x**(5/2)/5

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.207857, size = 7, normalized size = 0.78 \[ \frac{2}{5} \, x^{\frac{5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(3/2),x, algorithm="giac")

[Out]

2/5*x^(5/2)