Optimal. Leaf size=21 \[ \frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1) \]
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Rubi [A] time = 0.0073871, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {1350, 632, 31} \[ \frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1) \]
Antiderivative was successfully verified.
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Rule 1350
Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{13+\frac{2}{x}+15 x} \, dx &=\int \frac{x}{2+13 x+15 x^2} \, dx\\ &=-\left (\frac{3}{7} \int \frac{1}{3+15 x} \, dx\right )+\frac{10}{7} \int \frac{1}{10+15 x} \, dx\\ &=\frac{2}{21} \log (2+3 x)-\frac{1}{35} \log (1+5 x)\\ \end{align*}
Mathematica [A] time = 0.0029758, size = 21, normalized size = 1. \[ \frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 18, normalized size = 0.9 \begin{align*}{\frac{2\,\ln \left ( 2+3\,x \right ) }{21}}-{\frac{\ln \left ( 1+5\,x \right ) }{35}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.998803, size = 23, normalized size = 1.1 \begin{align*} -\frac{1}{35} \, \log \left (5 \, x + 1\right ) + \frac{2}{21} \, \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 = 1.25802, size = 54, normalized size = 2.57 \begin{align*} -\frac{1}{35} \, \log \left (5 \, x + 1\right ) + \frac{2}{21} \, \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 = 0.098802, size = 17, normalized size = 0.81 \begin{align*} - \frac{\log{\left (x + \frac{1}{5} \right )}}{35} + \frac{2 \log{\left (x + \frac{2}{3} \right )}}{21} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15851, size = 26, normalized size = 1.24 \begin{align*} -\frac{1}{35} \, \log \left ({\left | 5 \, x + 1 \right |}\right ) + \frac{2}{21} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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