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

Optimal result

Integrand size = 9, antiderivative size = 11 \[ \int \left (1-\sqrt {x}\right ) \, dx=x-\frac {2 x^{3/2}}{3} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (1-\sqrt {x}\right ) \, dx=x-\frac {2 x^{3/2}}{3} \]

[In]

Int[1 - Sqrt[x],x]

[Out]

x - (2*x^(3/2))/3

Rubi steps \begin{align*} \text {integral}& = x-\frac {2 x^{3/2}}{3} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \left (1-\sqrt {x}\right ) \, dx=x-\frac {2 x^{3/2}}{3} \]

[In]

Integrate[1 - Sqrt[x],x]

[Out]

x - (2*x^(3/2))/3

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 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	\(x -\frac {2 x^{\frac {3}{2}}}{3}\)	\(8\)
parts	\(x -\frac {2 x^{\frac {3}{2}}}{3}\)	\(8\)
trager	\(x -1-\frac {2 x^{\frac {3}{2}}}{3}\)	\(9\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \left (1-\sqrt {x}\right ) \, dx=-\frac {2}{3} \, x^{\frac {3}{2}} + x \]

[In]

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

[Out]

-2/3*x^(3/2) + x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \left (1-\sqrt {x}\right ) \, dx=- \frac {2 x^{\frac {3}{2}}}{3} + x \]

[In]

integrate(1-x**(1/2),x)

[Out]

-2*x**(3/2)/3 + x

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \left (1-\sqrt {x}\right ) \, dx=-\frac {2}{3} \, x^{\frac {3}{2}} + x \]

[In]

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

[Out]

-2/3*x^(3/2) + x

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \left (1-\sqrt {x}\right ) \, dx=-\frac {2}{3} \, x^{\frac {3}{2}} + x \]

[In]

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

[Out]

-2/3*x^(3/2) + x

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \left (1-\sqrt {x}\right ) \, dx=x-\frac {2\,x^{3/2}}{3} \]

[In]

int(1 - x^(1/2),x)

[Out]

x - (2*x^(3/2))/3