Optimal. Leaf size=21 \[ -\frac {2 a}{3 x^{3/2}}-\frac {2 b}{5 x^{5/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 21, 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} \[ -\frac {2 a}{3 x^{3/2}}-\frac {2 b}{5 x^{5/2}} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+\frac {b}{x}}{x^{5/2}} \, dx &=\int \left (\frac {b}{x^{7/2}}+\frac {a}{x^{5/2}}\right ) \, dx\\ &=-\frac {2 b}{5 x^{5/2}}-\frac {2 a}{3 x^{3/2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.81 \[ -\frac {2 (5 a x+3 b)}{15 x^{5/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.98, size = 13, normalized size = 0.62 \[ -\frac {2 \, {\left (5 \, a x + 3 \, b\right )}}{15 \, x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.62 \[ -\frac {2 \, {\left (5 \, a x + 3 \, b\right )}}{15 \, x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.67 \[ -\frac {2 \left (5 a x +3 b \right )}{15 x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.02, size = 13, normalized size = 0.62 \[ -\frac {2 \, a}{3 \, x^{\frac {3}{2}}} - \frac {2 \, b}{5 \, x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.62 \[ -\frac {6\,b+10\,a\,x}{15\,x^{5/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.94, size = 20, normalized size = 0.95 \[ - \frac {2 a}{3 x^{\frac {3}{2}}} - \frac {2 b}{5 x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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