Optimal. Leaf size=21 \[ \frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2) \]
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Rubi [A] time = 0.0104293, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188, Rules used = {1386, 616, 31} \[ \frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 1386
Rule 616
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{x \left (13+\frac{2}{x}+15 x\right )} \, dx &=\int \frac{1}{2+13 x+15 x^2} \, dx\\ &=\frac{15}{7} \int \frac{1}{3+15 x} \, dx-\frac{15}{7} \int \frac{1}{10+15 x} \, dx\\ &=-\frac{1}{7} \log (2+3 x)+\frac{1}{7} \log (1+5 x)\\ \end{align*}
Mathematica [A] time = 0.0026965, size = 21, normalized size = 1. \[ \frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 18, normalized size = 0.9 \begin{align*} -{\frac{\ln \left ( 2+3\,x \right ) }{7}}+{\frac{\ln \left ( 1+5\,x \right ) }{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00946, size = 23, normalized size = 1.1 \begin{align*} \frac{1}{7} \, \log \left (5 \, x + 1\right ) - \frac{1}{7} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.25171, size = 50, normalized size = 2.38 \begin{align*} \frac{1}{7} \, \log \left (5 \, x + 1\right ) - \frac{1}{7} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.095938, size = 15, normalized size = 0.71 \begin{align*} \frac{\log{\left (x + \frac{1}{5} \right )}}{7} - \frac{\log{\left (x + \frac{2}{3} \right )}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1028, size = 26, normalized size = 1.24 \begin{align*} \frac{1}{7} \, \log \left ({\left | 5 \, x + 1 \right |}\right ) - \frac{1}{7} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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