Optimal. Leaf size=19 \[ -\frac {2 a}{3 x^{3/2}}-\frac {2 b}{\sqrt {x}} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \begin {gather*} -\frac {2 a}{3 x^{3/2}}-\frac {2 b}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{x^{5/2}} \, dx &=\int \left (\frac {a}{x^{5/2}}+\frac {b}{x^{3/2}}\right ) \, dx\\ &=-\frac {2 a}{3 x^{3/2}}-\frac {2 b}{\sqrt {x}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.79 \begin {gather*} -\frac {2 (a+3 b x)}{3 x^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 15, normalized size = 0.79 \begin {gather*} -\frac {2 (a+3 b x)}{3 x^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 11, normalized size = 0.58 \begin {gather*} -\frac {2 \, {\left (3 \, b x + a\right )}}{3 \, x^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.97, size = 11, normalized size = 0.58 \begin {gather*} -\frac {2 \, {\left (3 \, b x + a\right )}}{3 \, x^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 0.63 \begin {gather*} -\frac {2 \left (3 b x +a \right )}{3 x^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 11, normalized size = 0.58 \begin {gather*} -\frac {2 \, {\left (3 \, b x + a\right )}}{3 \, x^{\frac {3}{2}}} \end {gather*}
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 \begin {gather*} -\frac {2\,a+6\,b\,x}{3\,x^{3/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.56, size = 19, normalized size = 1.00 \begin {gather*} - \frac {2 a}{3 x^{\frac {3}{2}}} - \frac {2 b}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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