Optimal. Leaf size=21 \[ -\frac{2 (35 x+29)}{\sqrt{3 x^2+5 x+2}} \]
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Rubi [A] time = 0.0049068, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {636} \[ -\frac{2 (35 x+29)}{\sqrt{3 x^2+5 x+2}} \]
Antiderivative was successfully verified.
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Rule 636
Rubi steps
\begin{align*} \int \frac{5-x}{\left (2+5 x+3 x^2\right )^{3/2}} \, dx &=-\frac{2 (29+35 x)}{\sqrt{2+5 x+3 x^2}}\\ \end{align*}
Mathematica [A] time = 0.052172, size = 21, normalized size = 1. \[ -\frac{2 (35 x+29)}{\sqrt{3 x^2+5 x+2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 28, normalized size = 1.3 \begin{align*} -2\,{\frac{ \left ( 29+35\,x \right ) \left ( 1+x \right ) \left ( 2+3\,x \right ) }{ \left ( 3\,{x}^{2}+5\,x+2 \right ) ^{3/2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03045, size = 41, normalized size = 1.95 \begin{align*} -\frac{70 \, x}{\sqrt{3 \, x^{2} + 5 \, x + 2}} - \frac{58}{\sqrt{3 \, x^{2} + 5 \, x + 2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.87837, size = 51, normalized size = 2.43 \begin{align*} -\frac{2 \,{\left (35 \, x + 29\right )}}{\sqrt{3 \, x^{2} + 5 \, x + 2}} \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}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int - \frac{5}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \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 = 1.09593, size = 26, normalized size = 1.24 \begin{align*} -\frac{2 \,{\left (35 \, x + 29\right )}}{\sqrt{3 \, x^{2} + 5 \, x + 2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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