Optimal. Leaf size=27 \[ \frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1) \]
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Rubi [A] time = 0.0157206, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.312, Rules used = {1386, 705, 29, 632, 31} \[ \frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1) \]
Antiderivative was successfully verified.
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Rule 1386
Rule 705
Rule 29
Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{x^2 \left (13+\frac{2}{x}+15 x\right )} \, dx &=\int \frac{1}{x \left (2+13 x+15 x^2\right )} \, dx\\ &=\frac{1}{2} \int \frac{1}{x} \, dx+\frac{1}{2} \int \frac{-13-15 x}{2+13 x+15 x^2} \, dx\\ &=\frac{\log (x)}{2}+\frac{45}{14} \int \frac{1}{10+15 x} \, dx-\frac{75}{7} \int \frac{1}{3+15 x} \, dx\\ &=\frac{\log (x)}{2}+\frac{3}{14} \log (2+3 x)-\frac{5}{7} \log (1+5 x)\\ \end{align*}
Mathematica [A] time = 0.0044054, size = 27, normalized size = 1. \[ \frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 22, normalized size = 0.8 \begin{align*}{\frac{\ln \left ( x \right ) }{2}}+{\frac{3\,\ln \left ( 2+3\,x \right ) }{14}}-{\frac{5\,\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 = 0.997671, size = 28, normalized size = 1.04 \begin{align*} -\frac{5}{7} \, \log \left (5 \, x + 1\right ) + \frac{3}{14} \, \log \left (3 \, x + 2\right ) + \frac{1}{2} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.2219, size = 70, normalized size = 2.59 \begin{align*} -\frac{5}{7} \, \log \left (5 \, x + 1\right ) + \frac{3}{14} \, \log \left (3 \, x + 2\right ) + \frac{1}{2} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.127447, size = 24, normalized size = 0.89 \begin{align*} \frac{\log{\left (x \right )}}{2} - \frac{5 \log{\left (x + \frac{1}{5} \right )}}{7} + \frac{3 \log{\left (x + \frac{2}{3} \right )}}{14} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14009, size = 32, normalized size = 1.19 \begin{align*} -\frac{5}{7} \, \log \left ({\left | 5 \, x + 1 \right |}\right ) + \frac{3}{14} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac{1}{2} \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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