Optimal. Leaf size=22 \[ -\frac{12-7 x}{9 \sqrt{6 x-x^2}} \]
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Rubi [A] time = 0.0047028, antiderivative size = 22, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0100448, size = 19, normalized size = 0.86 \[ \frac{7 x-12}{9 \sqrt{-(x-6) x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 23, normalized size = 1.1 \begin{align*} -{\frac{x \left ( -6+x \right ) \left ( -12+7\,x \right ) }{9} \left ( -{x}^{2}+6\,x \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03403, size = 38, normalized size = 1.73 \begin{align*} \frac{7 \, x}{9 \, \sqrt{-x^{2} + 6 \, x}} - \frac{4}{3 \, \sqrt{-x^{2} + 6 \, x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4443, size = 62, normalized size = 2.82 \begin{align*} -\frac{\sqrt{-x^{2} + 6 \, x}{\left (7 \, x - 12\right )}}{9 \,{\left (x^{2} - 6 \, x\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x + 4}{\left (- x \left (x - 6\right )\right )^{\frac{3}{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12045, size = 36, normalized size = 1.64 \begin{align*} -\frac{\sqrt{-x^{2} + 6 \, x}{\left (7 \, x - 12\right )}}{9 \,{\left (x^{2} - 6 \, x\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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