Optimal. Leaf size=22 \[ \frac {2 x^{3/2}}{3 a (a-b x)^{3/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 22, 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} \[ \frac {2 x^{3/2}}{3 a (a-b x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {\sqrt {x}}{(a-b x)^{5/2}} \, dx &=\frac {2 x^{3/2}}{3 a (a-b x)^{3/2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \[ \frac {2 x^{3/2}}{3 a (a-b x)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.42, size = 34, normalized size = 1.55 \[ \frac {2 \, \sqrt {-b x + a} x^{\frac {3}{2}}}{3 \, {\left (a b^{2} x^{2} - 2 \, a^{2} b x + a^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.63, size = 102, normalized size = 4.64 \[ \frac {4 \, {\left (3 \, {\left (\sqrt {-b x + a} \sqrt {-b} - \sqrt {{\left (b x - a\right )} b + a b}\right )}^{4} \sqrt {-b} + a^{2} \sqrt {-b} b^{2}\right )} {\left | b \right |}}{3 \, {\left ({\left (\sqrt {-b x + a} \sqrt {-b} - \sqrt {{\left (b x - a\right )} b + a b}\right )}^{2} - a b\right )}^{3} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.77 \[ \frac {2 x^{\frac {3}{2}}}{3 \left (-b x +a \right )^{\frac {3}{2}} a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 16, normalized size = 0.73 \[ \frac {2 \, x^{\frac {3}{2}}}{3 \, {\left (-b x + a\right )}^{\frac {3}{2}} a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 37, normalized size = 1.68 \[ \frac {2\,x^{3/2}\,\sqrt {a-b\,x}}{3\,\left (a^3-2\,a^2\,b\,x+a\,b^2\,x^2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.51, size = 95, normalized size = 4.32 \[ \begin {cases} \frac {2 i x^{\frac {3}{2}}}{- 3 a^{\frac {5}{2}} \sqrt {-1 + \frac {b x}{a}} + 3 a^{\frac {3}{2}} b x \sqrt {-1 + \frac {b x}{a}}} & \text {for}\: \left |{\frac {b x}{a}}\right | > 1 \\- \frac {2 x^{\frac {3}{2}}}{- 3 a^{\frac {5}{2}} \sqrt {1 - \frac {b x}{a}} + 3 a^{\frac {3}{2}} b x \sqrt {1 - \frac {b x}{a}}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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