Optimal. Leaf size=22 \[ -\frac {12-7 x}{9 \sqrt {6 x-x^2}} \]
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Rubi [A] time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {636} \[ -\frac {12-7 x}{9 \sqrt {6 x-x^2}} \]
Antiderivative was successfully verified.
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Rule 636
Rubi steps
\begin {align*} \int \frac {4+x}{\left (6 x-x^2\right )^{3/2}} \, dx &=-\frac {12-7 x}{9 \sqrt {6 x-x^2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 0.86 \[ \frac {7 x-12}{9 \sqrt {-((x-6) x)}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 27, normalized size = 1.23 \[ -\frac {\sqrt {-x^{2} + 6 \, x} {\left (7 \, x - 12\right )}}{9 \, {\left (x^{2} - 6 \, x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.52, size = 27, normalized size = 1.23 \[ -\frac {\sqrt {-x^{2} + 6 \, x} {\left (7 \, x - 12\right )}}{9 \, {\left (x^{2} - 6 \, x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 1.05 \[ -\frac {\left (x -6\right ) \left (7 x -12\right ) x}{9 \left (-x^{2}+6 x \right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 28, normalized size = 1.27 \[ \frac {7 \, x}{9 \, \sqrt {-x^{2} + 6 \, x}} - \frac {4}{3 \, \sqrt {-x^{2} + 6 \, x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.50, size = 18, normalized size = 0.82 \[ \frac {7\,x-12}{9\,\sqrt {6\,x-x^2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x + 4}{\left (- x \left (x - 6\right )\right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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