Optimal. Leaf size=21 \[ -\frac{\tan ^{-1}\left (\frac{2-3 x}{\sqrt{6}}\right )}{3 \sqrt{6}} \]
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Rubi [A] time = 0.0170595, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {618, 204} \[ -\frac{\tan ^{-1}\left (\frac{2-3 x}{\sqrt{6}}\right )}{3 \sqrt{6}} \]
Antiderivative was successfully verified.
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Rule 618
Rule 204
Rubi steps
\begin{align*} \int \frac{1}{10-12 x+9 x^2} \, dx &=-\left (2 \operatorname{Subst}\left (\int \frac{1}{-216-x^2} \, dx,x,-12+18 x\right )\right )\\ &=-\frac{\tan ^{-1}\left (\frac{2-3 x}{\sqrt{6}}\right )}{3 \sqrt{6}}\\ \end{align*}
Mathematica [A] time = 0.008068, size = 21, normalized size = 1. \[ \frac{\tan ^{-1}\left (\frac{3 x-2}{\sqrt{6}}\right )}{3 \sqrt{6}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 17, normalized size = 0.8 \begin{align*}{\frac{\sqrt{6}}{18}\arctan \left ({\frac{ \left ( 18\,x-12 \right ) \sqrt{6}}{36}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.41101, size = 22, normalized size = 1.05 \begin{align*} \frac{1}{18} \, \sqrt{6} \arctan \left (\frac{1}{6} \, \sqrt{6}{\left (3 \, x - 2\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.83148, size = 59, normalized size = 2.81 \begin{align*} \frac{1}{18} \, \sqrt{6} \arctan \left (\frac{1}{6} \, \sqrt{6}{\left (3 \, x - 2\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.104321, size = 22, normalized size = 1.05 \begin{align*} \frac{\sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x}{2} - \frac{\sqrt{6}}{3} \right )}}{18} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0824, size = 22, normalized size = 1.05 \begin{align*} \frac{1}{18} \, \sqrt{6} \arctan \left (\frac{1}{6} \, \sqrt{6}{\left (3 \, x - 2\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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