Optimal. Leaf size=17 \[ -\frac {2}{\sqrt {x}}+\frac {2 x^{5/2}}{5} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \frac {2 x^{5/2}}{5}-\frac {2}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rubi steps
\begin {align*} \int \left (\frac {1}{x^{3/2}}+x^{3/2}\right ) \, dx &=-\frac {2}{\sqrt {x}}+\frac {2 x^{5/2}}{5}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 14, normalized size = 0.82 \begin {gather*} \frac {2 \left (-5+x^3\right )}{5 \sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.03, size = 12, normalized size = 0.71
method | result | size |
gosper | \(\frac {\frac {2 x^{3}}{5}-2}{\sqrt {x}}\) | \(11\) |
trager | \(\frac {\frac {2 x^{3}}{5}-2}{\sqrt {x}}\) | \(11\) |
derivativedivides | \(\frac {2 x^{\frac {5}{2}}}{5}-\frac {2}{\sqrt {x}}\) | \(12\) |
default | \(\frac {2 x^{\frac {5}{2}}}{5}-\frac {2}{\sqrt {x}}\) | \(12\) |
risch | \(\frac {2 x^{\frac {5}{2}}}{5}-\frac {2}{\sqrt {x}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 11, normalized size = 0.65 \begin {gather*} \frac {2}{5} \, x^{\frac {5}{2}} - \frac {2}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.95, size = 10, normalized size = 0.59 \begin {gather*} \frac {2 \, {\left (x^{3} - 5\right )}}{5 \, \sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 14, normalized size = 0.82 \begin {gather*} \frac {2 x^{\frac {5}{2}}}{5} - \frac {2}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.66, size = 11, normalized size = 0.65 \begin {gather*} \frac {2}{5} \, x^{\frac {5}{2}} - \frac {2}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 12, normalized size = 0.71 \begin {gather*} \frac {2\,x^3-10}{5\,\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________