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

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

[Out]

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

________________________________________________________________________________________

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 = {} \[ x-\frac {2 x^{3/2}}{3} \]

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 = 0.00, size = 11, normalized size = 1.00 \[ x-\frac {2 x^{3/2}}{3} \]

Antiderivative was successfully verified.

[In]

Integrate[1 - Sqrt[x],x]

[Out]

x - (2*x^(3/2))/3

________________________________________________________________________________________

fricas [A]  time = 0.41, size = 7, normalized size = 0.64 \[ -\frac {2}{3} \, x^{\frac {3}{2}} + x \]

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

________________________________________________________________________________________

giac [A]  time = 0.36, size = 7, normalized size = 0.64 \[ -\frac {2}{3} \, x^{\frac {3}{2}} + x \]

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

________________________________________________________________________________________

maple [A]  time = 0.00, 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]

int(1-x^(1/2),x)

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.90, size = 7, normalized size = 0.64 \[ -\frac {2}{3} \, x^{\frac {3}{2}} + x \]

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

________________________________________________________________________________________

mupad [B]  time = 0.03, size = 7, normalized size = 0.64 \[ x-\frac {2\,x^{3/2}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - x^(1/2),x)

[Out]

x - (2*x^(3/2))/3

________________________________________________________________________________________

sympy [A]  time = 0.06, 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

________________________________________________________________________________________