3.952 \(\int (1-\sqrt{x}) \, dx\)

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 = 0.0011952, 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., Rules used = {} \[ x-\frac{2 x^{3/2}}{3} \]

Antiderivative was successfully verified.

[In]

Int[1 - Sqrt[x],x]

[Out]

x - (2*x^(3/2))/3

Rubi steps

\begin{align*} \int \left (1-\sqrt{x}\right ) \, dx &=x-\frac{2 x^{3/2}}{3}\\ \end{align*}

Mathematica [A]  time = 0.0008729, 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., size = 8, normalized size = 0.7 \begin{align*} x-{\frac{2}{3}{x}^{{\frac{3}{2}}}} \end{align*}

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 = 0.99302, size = 9, normalized size = 0.82 \begin{align*} -\frac{2}{3} \, x^{\frac{3}{2}} + x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1-x^(1/2),x, algorithm="maxima")

[Out]

-2/3*x^(3/2) + x

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Fricas [A]  time = 1.69338, size = 24, normalized size = 2.18 \begin{align*} -\frac{2}{3} \, x^{\frac{3}{2}} + x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1-x^(1/2),x, algorithm="fricas")

[Out]

-2/3*x^(3/2) + x

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Sympy [A]  time = 0.054076, size = 8, normalized size = 0.73 \begin{align*} - \frac{2 x^{\frac{3}{2}}}{3} + x \end{align*}

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 [A]  time = 1.22417, size = 9, normalized size = 0.82 \begin{align*} -\frac{2}{3} \, x^{\frac{3}{2}} + x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1-x^(1/2),x, algorithm="giac")

[Out]

-2/3*x^(3/2) + x