Optimal. Leaf size=21 \[ \frac{1}{7} \log (3 x+1)-\frac{1}{7} \log (2-x) \]
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Rubi [A] time = 0.0055975, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {616, 31} \[ \frac{1}{7} \log (3 x+1)-\frac{1}{7} \log (2-x) \]
Antiderivative was successfully verified.
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Rule 616
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{2+5 x-3 x^2} \, dx &=-\left (\frac{3}{7} \int \frac{1}{-1-3 x} \, dx\right )+\frac{3}{7} \int \frac{1}{6-3 x} \, dx\\ &=-\frac{1}{7} \log (2-x)+\frac{1}{7} \log (1+3 x)\\ \end{align*}
Mathematica [A] time = 0.0029986, size = 21, normalized size = 1. \[ \frac{1}{7} \log (3 x+1)-\frac{1}{7} \log (2-x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.049, size = 16, normalized size = 0.8 \begin{align*}{\frac{\ln \left ( 1+3\,x \right ) }{7}}-{\frac{\ln \left ( -2+x \right ) }{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09327, size = 20, normalized size = 0.95 \begin{align*} \frac{1}{7} \, \log \left (3 \, x + 1\right ) - \frac{1}{7} \, \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.14062, size = 47, normalized size = 2.24 \begin{align*} \frac{1}{7} \, \log \left (3 \, x + 1\right ) - \frac{1}{7} \, \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.16336, size = 14, normalized size = 0.67 \begin{align*} - \frac{\log{\left (x - 2 \right )}}{7} + \frac{\log{\left (x + \frac{1}{3} \right )}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20764, size = 23, normalized size = 1.1 \begin{align*} \frac{1}{7} \, \log \left ({\left | 3 \, x + 1 \right |}\right ) - \frac{1}{7} \, \log \left ({\left | x - 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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