Optimal. Leaf size=19 \[ \frac {2 x^2}{5 b \sqrt {\frac {b}{x}}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac {2 x^2}{5 b \sqrt {\frac {b}{x}}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\left (\frac {b}{x}\right )^{3/2}} \, dx &=\frac {\int x^{3/2} \, dx}{b \sqrt {\frac {b}{x}} \sqrt {x}}\\ &=\frac {2 x^2}{5 b \sqrt {\frac {b}{x}}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 0.74 \[ \frac {2 x}{5 \left (\frac {b}{x}\right )^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.92, size = 15, normalized size = 0.79 \[ \frac {2 \, x^{3} \sqrt {\frac {b}{x}}}{5 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 15, normalized size = 0.79 \[ \frac {2 \, x^{2}}{5 \, b \sqrt {\frac {b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 11, normalized size = 0.58 \[ \frac {2 x}{5 \left (\frac {b}{x}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.32, size = 10, normalized size = 0.53 \[ \frac {2 \, x}{5 \, \left (\frac {b}{x}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.94, size = 15, normalized size = 0.79 \[ \frac {2\,x^3\,\sqrt {\frac {b}{x}}}{5\,b^2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.50, size = 15, normalized size = 0.79 \[ \frac {2 x}{5 b^{\frac {3}{2}} \left (\frac {1}{x}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________