Optimal. Leaf size=14 \[ \frac {x}{2 \sqrt {\frac {b}{x^2}}} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 14, 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} \begin {gather*} \frac {x}{2 \sqrt {\frac {b}{x^2}}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {\frac {b}{x^2}}} \, dx &=\frac {\int x \, dx}{\sqrt {\frac {b}{x^2}} x}\\ &=\frac {x}{2 \sqrt {\frac {b}{x^2}}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {x}{2 \sqrt {\frac {b}{x^2}}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 1.68, size = 19, normalized size = 1.36 \begin {gather*} \frac {x^3 \sqrt {\frac {b}{x^2}}}{2 b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.11, size = 15, normalized size = 1.07 \begin {gather*} \frac {x^{3} \sqrt {\frac {b}{x^{2}}}}{2 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 12, normalized size = 0.86 \begin {gather*} \frac {x^{2}}{2 \, \sqrt {b} \mathrm {sgn}\relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 11, normalized size = 0.79 \begin {gather*} \frac {x}{2 \sqrt {\frac {b}{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.30, size = 10, normalized size = 0.71 \begin {gather*} \frac {x}{2 \, \sqrt {\frac {b}{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.93, size = 13, normalized size = 0.93 \begin {gather*} \frac {x^3\,\sqrt {\frac {1}{x^2}}}{2\,\sqrt {b}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.39, size = 15, normalized size = 1.07 \begin {gather*} \frac {x}{2 \sqrt {b} \sqrt {\frac {1}{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________