3.22 \(\int \sqrt{x} \, dx\)

Optimal. Leaf size=9 \[ \frac{2 x^{3/2}}{3} \]

[Out]

(2*x^(3/2))/3

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Rubi [A]  time = 0.00290737, 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 \[ \frac{2 x^{3/2}}{3} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[x],x]

[Out]

(2*x^(3/2))/3

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Rubi in Sympy [A]  time = 0.907799, size = 7, normalized size = 0.78 \[ \frac{2 x^{\frac{3}{2}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**(1/2),x)

[Out]

2*x**(3/2)/3

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Mathematica [A]  time = 0.000781718, size = 9, normalized size = 1. \[ \frac{2 x^{3/2}}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[x],x]

[Out]

(2*x^(3/2))/3

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Maple [A]  time = 0.003, size = 6, normalized size = 0.7 \[{\frac{2}{3}{x}^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^(1/2),x)

[Out]

2/3*x^(3/2)

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Maxima [A]  time = 1.34213, size = 7, normalized size = 0.78 \[ \frac{2}{3} \, x^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(x),x, algorithm="maxima")

[Out]

2/3*x^(3/2)

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Fricas [A]  time = 0.197406, size = 7, normalized size = 0.78 \[ \frac{2}{3} \, x^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(x),x, algorithm="fricas")

[Out]

2/3*x^(3/2)

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Sympy [A]  time = 0.02884, size = 7, normalized size = 0.78 \[ \frac{2 x^{\frac{3}{2}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**(1/2),x)

[Out]

2*x**(3/2)/3

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GIAC/XCAS [A]  time = 0.207322, size = 7, normalized size = 0.78 \[ \frac{2}{3} \, x^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(x),x, algorithm="giac")

[Out]

2/3*x^(3/2)