Optimal. Leaf size=17 \[ -\frac {\sqrt {2-b x}}{\sqrt {x}} \]
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Rubi [A] time = 0.00, antiderivative size = 17, 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 {\sqrt {2-b x}}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {1}{x^{3/2} \sqrt {2-b x}} \, dx &=-\frac {\sqrt {2-b x}}{\sqrt {x}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {\sqrt {2-b x}}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 17, normalized size = 1.00 \begin {gather*} -\frac {\sqrt {2-b x}}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.13, size = 13, normalized size = 0.76 \begin {gather*} -\frac {\sqrt {-b x + 2}}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.28, size = 30, normalized size = 1.76 \begin {gather*} -\frac {\sqrt {-b x + 2} b^{2}}{\sqrt {{\left (b x - 2\right )} b + 2 \, b} {\left | b \right |}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.82 \begin {gather*} -\frac {\sqrt {-b x +2}}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 13, normalized size = 0.76 \begin {gather*} -\frac {\sqrt {-b x + 2}}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.31, size = 13, normalized size = 0.76 \begin {gather*} -\frac {\sqrt {2-b\,x}}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.93, size = 39, normalized size = 2.29 \begin {gather*} \begin {cases} - \sqrt {b} \sqrt {-1 + \frac {2}{b x}} & \text {for}\: \frac {2}{\left |{b x}\right |} > 1 \\- i \sqrt {b} \sqrt {1 - \frac {2}{b x}} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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