Optimal. Leaf size=19 \[ -\frac {a}{2 x^2}-\frac {2 b}{3 x^{3/2}} \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14} \[ -\frac {a}{2 x^2}-\frac {2 b}{3 x^{3/2}} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b \sqrt {x}}{x^3} \, dx &=\int \left (\frac {a}{x^3}+\frac {b}{x^{5/2}}\right ) \, dx\\ &=-\frac {a}{2 x^2}-\frac {2 b}{3 x^{3/2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \[ -\frac {a}{2 x^2}-\frac {2 b}{3 x^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.98, size = 15, normalized size = 0.79 \[ -\frac {4 \, b \sqrt {x} + 3 \, a}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 15, normalized size = 0.79 \[ -\frac {4 \, b \sqrt {x} + 3 \, a}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.74 \[ -\frac {2 b}{3 x^{\frac {3}{2}}}-\frac {a}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.84, size = 15, normalized size = 0.79 \[ -\frac {4 \, b \sqrt {x} + 3 \, a}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.68 \[ -\frac {a}{2\,x^2}-\frac {2\,b}{3\,x^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.66, size = 17, normalized size = 0.89 \[ - \frac {a}{2 x^{2}} - \frac {2 b}{3 x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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