Optimal. Leaf size=21 \[ \frac{1}{8} \log (1-2 x)+\frac{3}{8} \log (2 x+7) \]
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Rubi [A] time = 0.0054708, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {632, 31} \[ \frac{1}{8} \log (1-2 x)+\frac{3}{8} \log (2 x+7) \]
Antiderivative was successfully verified.
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Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{1+2 x}{-7+12 x+4 x^2} \, dx &=\frac{1}{2} \int \frac{1}{-2+4 x} \, dx+\frac{3}{2} \int \frac{1}{14+4 x} \, dx\\ &=\frac{1}{8} \log (1-2 x)+\frac{3}{8} \log (7+2 x)\\ \end{align*}
Mathematica [A] time = 0.0040953, size = 21, normalized size = 1. \[ \frac{1}{8} \log (1-2 x)+\frac{3}{8} \log (2 x+7) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 18, normalized size = 0.9 \begin{align*}{\frac{3\,\ln \left ( 7+2\,x \right ) }{8}}+{\frac{\ln \left ( 2\,x-1 \right ) }{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.943763, size = 23, normalized size = 1.1 \begin{align*} \frac{3}{8} \, \log \left (2 \, x + 7\right ) + \frac{1}{8} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.86837, size = 50, normalized size = 2.38 \begin{align*} \frac{3}{8} \, \log \left (2 \, x + 7\right ) + \frac{1}{8} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.122183, size = 17, normalized size = 0.81 \begin{align*} \frac{\log{\left (x - \frac{1}{2} \right )}}{8} + \frac{3 \log{\left (x + \frac{7}{2} \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05618, size = 26, normalized size = 1.24 \begin{align*} \frac{3}{8} \, \log \left ({\left | 2 \, x + 7 \right |}\right ) + \frac{1}{8} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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