Optimal. Leaf size=19 \[ \frac{7}{11} \log (3-2 x)-\frac{7}{11} \log (x+4) \]
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Rubi [A] time = 0.0066137, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214, Rules used = {12, 616, 31} \[ \frac{7}{11} \log (3-2 x)-\frac{7}{11} \log (x+4) \]
Antiderivative was successfully verified.
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Rule 12
Rule 616
Rule 31
Rubi steps
\begin{align*} \int \frac{7}{-12+5 x+2 x^2} \, dx &=7 \int \frac{1}{-12+5 x+2 x^2} \, dx\\ &=\frac{14}{11} \int \frac{1}{-3+2 x} \, dx-\frac{14}{11} \int \frac{1}{8+2 x} \, dx\\ &=\frac{7}{11} \log (3-2 x)-\frac{7}{11} \log (4+x)\\ \end{align*}
Mathematica [A] time = 0.0033927, size = 21, normalized size = 1.11 \[ 7 \left (\frac{1}{11} \log (3-2 x)-\frac{1}{11} \log (x+4)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 16, normalized size = 0.8 \begin{align*}{\frac{7\,\ln \left ( -3+2\,x \right ) }{11}}-{\frac{7\,\ln \left ( 4+x \right ) }{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.919794, size = 20, normalized size = 1.05 \begin{align*} \frac{7}{11} \, \log \left (2 \, x - 3\right ) - \frac{7}{11} \, \log \left (x + 4\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.88224, size = 50, normalized size = 2.63 \begin{align*} \frac{7}{11} \, \log \left (2 \, x - 3\right ) - \frac{7}{11} \, \log \left (x + 4\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.090972, size = 17, normalized size = 0.89 \begin{align*} \frac{7 \log{\left (x - \frac{3}{2} \right )}}{11} - \frac{7 \log{\left (x + 4 \right )}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05879, size = 23, normalized size = 1.21 \begin{align*} \frac{7}{11} \, \log \left ({\left | 2 \, x - 3 \right |}\right ) - \frac{7}{11} \, \log \left ({\left | x + 4 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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