Optimal. Leaf size=16 \[ -\frac {\sqrt {b x+2}}{\sqrt {x}} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {37} \[ -\frac {\sqrt {b x+2}}{\sqrt {x}} \]
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 = 16, normalized size = 1.00 \[ -\frac {\sqrt {b x+2}}{\sqrt {x}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 12, normalized size = 0.75 \[ -\frac {\sqrt {b x + 2}}{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.11, size = 29, normalized size = 1.81 \[ -\frac {\sqrt {b x + 2} b^{2}}{\sqrt {{\left (b x + 2\right )} b - 2 \, b} {\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ -\frac {\sqrt {b x +2}}{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 12, normalized size = 0.75 \[ -\frac {\sqrt {b x + 2}}{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.33, size = 12, normalized size = 0.75 \[ -\frac {\sqrt {b\,x+2}}{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.88, size = 15, normalized size = 0.94 \[ - \sqrt {b} \sqrt {1 + \frac {2}{b x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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