3.10.52 \(\int (1-\sqrt {x}) \, dx\) [952]

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

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x-\frac {2 x^{3/2}}{3} \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} x-\frac {2 x^{3/2}}{3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 - Sqrt[x],x]

[Out]

x - (2*x^(3/2))/3

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Maple [A]
time = 0.02, size = 8, normalized size = 0.73

method	result	size
derivativedivides	\(x -\frac {2 x^{\frac {3}{2}}}{3}\)	\(8\)
default	\(x -\frac {2 x^{\frac {3}{2}}}{3}\)	\(8\)
risch	\(x -\frac {2 x^{\frac {3}{2}}}{3}\)	\(8\)
trager	\(-1+x -\frac {2 x^{\frac {3}{2}}}{3}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1-x^(1/2),x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.27, size = 7, normalized size = 0.64 \begin {gather*} -\frac {2}{3} \, x^{\frac {3}{2}} + x \end {gather*}

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 = 0.33, size = 7, normalized size = 0.64 \begin {gather*} -\frac {2}{3} \, x^{\frac {3}{2}} + x \end {gather*}

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 = 0.01, size = 8, normalized size = 0.73 \begin {gather*} - \frac {2 x^{\frac {3}{2}}}{3} + x \end {gather*}

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 = 3.15, size = 7, normalized size = 0.64 \begin {gather*} -\frac {2}{3} \, x^{\frac {3}{2}} + x \end {gather*}

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

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Mupad [B]
time = 0.00, size = 7, normalized size = 0.64 \begin {gather*} x-\frac {2\,x^{3/2}}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - x^(1/2),x)

[Out]

x - (2*x^(3/2))/3

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