Optimal. Leaf size=15 \[ \frac {\sqrt {x}}{\sqrt {b x+2}} \]
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Rubi [A] time = 0.00, antiderivative size = 15, 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} \[ \frac {\sqrt {x}}{\sqrt {b x+2}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {x} (2+b x)^{3/2}} \, dx &=\frac {\sqrt {x}}{\sqrt {2+b x}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {\sqrt {x}}{\sqrt {b x+2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 11, normalized size = 0.73 \[ \frac {\sqrt {x}}{\sqrt {b x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.22, size = 44, normalized size = 2.93 \[ \frac {4 \, b^{\frac {3}{2}}}{{\left ({\left (\sqrt {b x + 2} \sqrt {b} - \sqrt {{\left (b x + 2\right )} b - 2 \, b}\right )}^{2} + 2 \, b\right )} {\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 0.80 \[ \frac {\sqrt {x}}{\sqrt {b x +2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 11, normalized size = 0.73 \[ \frac {\sqrt {x}}{\sqrt {b x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.31, size = 11, normalized size = 0.73 \[ \frac {\sqrt {x}}{\sqrt {b\,x+2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.86, size = 15, normalized size = 1.00 \[ \frac {1}{\sqrt {b} \sqrt {1 + \frac {2}{b x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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