Optimal. Leaf size=9 \[ \frac {2 x^{3/2}}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {30}
\begin {gather*} \frac {2 x^{3/2}}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 30
Rubi steps
\begin {align*} \int \sqrt {x} \, dx &=\frac {2 x^{3/2}}{3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {2 x^{3/2}}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 6, normalized size = 0.67
method | result | size |
gosper | \(\frac {2 x^{\frac {3}{2}}}{3}\) | \(6\) |
derivativedivides | \(\frac {2 x^{\frac {3}{2}}}{3}\) | \(6\) |
default | \(\frac {2 x^{\frac {3}{2}}}{3}\) | \(6\) |
trager | \(\frac {2 x^{\frac {3}{2}}}{3}\) | \(6\) |
risch | \(\frac {2 x^{\frac {3}{2}}}{3}\) | \(6\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 5, normalized size = 0.56 \begin {gather*} \frac {2}{3} \, x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.80, size = 5, normalized size = 0.56 \begin {gather*} \frac {2}{3} \, x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 7, normalized size = 0.78 \begin {gather*} \frac {2 x^{\frac {3}{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.03, size = 5, normalized size = 0.56 \begin {gather*} \frac {2}{3} \, x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 5, normalized size = 0.56 \begin {gather*} \frac {2\,x^{3/2}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________