Optimal. Leaf size=18 \[ -\frac {(b x+2)^{3/2}}{3 x^{3/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 18, 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} \[ -\frac {(b x+2)^{3/2}}{3 x^{3/2}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {\sqrt {2+b x}}{x^{5/2}} \, dx &=-\frac {(2+b x)^{3/2}}{3 x^{3/2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 1.00 \[ -\frac {(b x+2)^{3/2}}{3 x^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 12, normalized size = 0.67 \[ -\frac {{\left (b x + 2\right )}^{\frac {3}{2}}}{3 \, x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.15, size = 29, normalized size = 1.61 \[ -\frac {{\left (b x + 2\right )}^{\frac {3}{2}} b^{4}}{3 \, {\left ({\left (b x + 2\right )} b - 2 \, b\right )}^{\frac {3}{2}} {\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.72 \[ -\frac {\left (b x +2\right )^{\frac {3}{2}}}{3 x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 12, normalized size = 0.67 \[ -\frac {{\left (b x + 2\right )}^{\frac {3}{2}}}{3 \, x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 18, normalized size = 1.00 \[ -\frac {\sqrt {b\,x+2}\,\left (\frac {b\,x}{3}+\frac {2}{3}\right )}{x^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.45, size = 37, normalized size = 2.06 \[ - \frac {b^{\frac {3}{2}} \sqrt {1 + \frac {2}{b x}}}{3} - \frac {2 \sqrt {b} \sqrt {1 + \frac {2}{b x}}}{3 x} \]
Verification of antiderivative is not currently implemented for this CAS.
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