Optimal. Leaf size=19 \[ \frac {x^{3/2}}{3 (2-b x)^{3/2}} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {37} \begin {gather*} \frac {x^{3/2}}{3 (2-b x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin {align*} \int \frac {\sqrt {x}}{(2-b x)^{5/2}} \, dx &=\frac {x^{3/2}}{3 (2-b x)^{3/2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} \frac {x^{3/2}}{3 (2-b x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.11, size = 26, normalized size = 1.37 \begin {gather*} \frac {x^{3/2} \sqrt {2-b x}}{3 (b x-2)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 1.03, size = 28, normalized size = 1.47 \begin {gather*} \frac {\sqrt {-b x + 2} x^{\frac {3}{2}}}{3 \, {\left (b^{2} x^{2} - 4 \, b x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 1.25, size = 95, normalized size = 5.00 \begin {gather*} \frac {4 \, {\left (3 \, {\left (\sqrt {-b x + 2} \sqrt {-b} - \sqrt {{\left (b x - 2\right )} b + 2 \, b}\right )}^{4} \sqrt {-b} + 4 \, \sqrt {-b} b^{2}\right )} {\left | b \right |}}{3 \, {\left ({\left (\sqrt {-b x + 2} \sqrt {-b} - \sqrt {{\left (b x - 2\right )} b + 2 \, b}\right )}^{2} - 2 \, b\right )}^{3} b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 14, normalized size = 0.74 \begin {gather*} \frac {x^{\frac {3}{2}}}{3 \left (-b x +2\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.38, size = 13, normalized size = 0.68 \begin {gather*} \frac {x^{\frac {3}{2}}}{3 \, {\left (-b x + 2\right )}^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.23, size = 13, normalized size = 0.68 \begin {gather*} \frac {x^{3/2}}{3\,{\left (2-b\,x\right )}^{3/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 1.46, size = 65, normalized size = 3.42 \begin {gather*} \begin {cases} \frac {i x^{\frac {3}{2}}}{3 b x \sqrt {b x - 2} - 6 \sqrt {b x - 2}} & \text {for}\: \frac {\left |{b x}\right |}{2} > 1 \\- \frac {x^{\frac {3}{2}}}{3 b x \sqrt {- b x + 2} - 6 \sqrt {- b x + 2}} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________