Optimal. Leaf size=17 \[ \frac {6}{5} \left (x-3 \sqrt {x}\right )^{5/3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.06, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2034, 629} \[ \frac {6}{5} \left (x-3 \sqrt {x}\right )^{5/3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 629
Rule 2034
Rubi steps
\begin {align*} \int \frac {\left (-3+2 \sqrt {x}\right ) \left (-3 \sqrt {x}+x\right )^{2/3}}{\sqrt {x}} \, dx &=2 \operatorname {Subst}\left (\int (-3+2 x) \left (-3 x+x^2\right )^{2/3} \, dx,x,\sqrt {x}\right )\\ &=\frac {6}{5} \left (-3 \sqrt {x}+x\right )^{5/3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 17, normalized size = 1.00 \[ \frac {6}{5} \left (x-3 \sqrt {x}\right )^{5/3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.46, size = 11, normalized size = 0.65 \[ \frac {6}{5} \, {\left (x - 3 \, \sqrt {x}\right )}^{\frac {5}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.37, size = 11, normalized size = 0.65 \[ \frac {6}{5} \, {\left (x - 3 \, \sqrt {x}\right )}^{\frac {5}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 12, normalized size = 0.71 \[ \frac {6 \left (x -3 \sqrt {x}\right )^{\frac {5}{3}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (x - 3 \, \sqrt {x}\right )}^{\frac {2}{3}} {\left (2 \, \sqrt {x} - 3\right )}}{\sqrt {x}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.70, size = 11, normalized size = 0.65 \[ \frac {6\,{\left (x-3\,\sqrt {x}\right )}^{5/3}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 1.27, size = 36, normalized size = 2.12 \[ - \frac {18 \sqrt {x} \left (- 3 \sqrt {x} + x\right )^{\frac {2}{3}}}{5} + \frac {6 x \left (- 3 \sqrt {x} + x\right )^{\frac {2}{3}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________