3.692 \(\int \left (1-\sqrt{x}\right ) \, dx\)

Optimal. Leaf size=11 \[ x-\frac{2 x^{3/2}}{3} \]

[Out]

x - (2*x^(3/2))/3

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Rubi [A]  time = 0.00568546, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ x-\frac{2 x^{3/2}}{3} \]

Antiderivative was successfully verified.

[In]  Int[1 - Sqrt[x],x]

[Out]

x - (2*x^(3/2))/3

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Rubi in Sympy [A]  time = 0.639337, size = 8, normalized size = 0.73 \[ - \frac{2 x^{\frac{3}{2}}}{3} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1-x**(1/2),x)

[Out]

-2*x**(3/2)/3 + x

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Mathematica [A]  time = 0.00252499, size = 11, normalized size = 1. \[ x-\frac{2 x^{3/2}}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[1 - Sqrt[x],x]

[Out]

x - (2*x^(3/2))/3

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Maple [A]  time = 0.001, size = 8, normalized size = 0.7 \[ x-{\frac{2}{3}{x}^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1-x^(1/2),x)

[Out]

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

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Maxima [A]  time = 0.680649, size = 9, normalized size = 0.82 \[ -\frac{2}{3} \, x^{\frac{3}{2}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-sqrt(x) + 1,x, algorithm="maxima")

[Out]

-2/3*x^(3/2) + x

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Fricas [A]  time = 0.26406, size = 9, normalized size = 0.82 \[ -\frac{2}{3} \, x^{\frac{3}{2}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-sqrt(x) + 1,x, algorithm="fricas")

[Out]

-2/3*x^(3/2) + x

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Sympy [A]  time = 0.06273, size = 8, normalized size = 0.73 \[ - \frac{2 x^{\frac{3}{2}}}{3} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1-x**(1/2),x)

[Out]

-2*x**(3/2)/3 + x

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GIAC/XCAS [A]  time = 0.265063, size = 9, normalized size = 0.82 \[ -\frac{2}{3} \, x^{\frac{3}{2}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-sqrt(x) + 1,x, algorithm="giac")

[Out]

-2/3*x^(3/2) + x