Optimal. Leaf size=17 \[ -\frac{\sin ^{-1}\left (\frac{1}{7} (5-6 x)\right )}{\sqrt{3}} \]
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Rubi [A] time = 0.006666, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {619, 216} \[ -\frac{\sin ^{-1}\left (\frac{1}{7} (5-6 x)\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
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Rule 619
Rule 216
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{2+5 x-3 x^2}} \, dx &=-\frac{\operatorname{Subst}\left (\int \frac{1}{\sqrt{1-\frac{x^2}{49}}} \, dx,x,5-6 x\right )}{7 \sqrt{3}}\\ &=-\frac{\sin ^{-1}\left (\frac{1}{7} (5-6 x)\right )}{\sqrt{3}}\\ \end{align*}
Mathematica [A] time = 0.0061719, size = 17, normalized size = 1. \[ -\frac{\sin ^{-1}\left (\frac{1}{7} (5-6 x)\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.049, size = 12, normalized size = 0.7 \begin{align*}{\frac{\sqrt{3}}{3}\arcsin \left ( -{\frac{5}{7}}+{\frac{6\,x}{7}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.70508, size = 15, normalized size = 0.88 \begin{align*} -\frac{1}{3} \, \sqrt{3} \arcsin \left (-\frac{6}{7} \, x + \frac{5}{7}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.9463, size = 115, normalized size = 6.76 \begin{align*} -\frac{1}{3} \, \sqrt{3} \arctan \left (\frac{\sqrt{3} \sqrt{-3 \, x^{2} + 5 \, x + 2}{\left (6 \, x - 5\right )}}{6 \,{\left (3 \, x^{2} - 5 \, x - 2\right )}}\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{1}{\sqrt{- 3 x^{2} + 5 x + 2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.3186, size = 15, normalized size = 0.88 \begin{align*} \frac{1}{3} \, \sqrt{3} \arcsin \left (\frac{6}{7} \, x - \frac{5}{7}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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