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 = 0.02, antiderivative size = 21, normalized size of antiderivative = 1.00, 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 204
Rule 618
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*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ \frac {\tan ^{-1}\left (\frac {3 x-2}{\sqrt {6}}\right )}{3 \sqrt {6}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 16, normalized size = 0.76 \[ \frac {1}{18} \, \sqrt {6} \arctan \left (\frac {1}{6} \, \sqrt {6} {\left (3 \, x - 2\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 16, normalized size = 0.76 \[ \frac {1}{18} \, \sqrt {6} \arctan \left (\frac {1}{6} \, \sqrt {6} {\left (3 \, x - 2\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.81 \[ \frac {\sqrt {6}\, \arctan \left (\frac {\left (18 x -12\right ) \sqrt {6}}{36}\right )}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.95, size = 16, normalized size = 0.76 \[ \frac {1}{18} \, \sqrt {6} \arctan \left (\frac {1}{6} \, \sqrt {6} {\left (3 \, x - 2\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 16, normalized size = 0.76 \[ \frac {\sqrt {6}\,\mathrm {atan}\left (\frac {\sqrt {6}\,\left (3\,x-2\right )}{6}\right )}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 22, normalized size = 1.05 \[ \frac {\sqrt {6} \operatorname {atan}{\left (\frac {\sqrt {6} x}{2} - \frac {\sqrt {6}}{3} \right )}}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
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