Optimal. Leaf size=23 \[ \frac{1}{7} \log \left (\frac{1}{x}+5\right )-\frac{1}{7} \log \left (\frac{2}{x}+3\right ) \]
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Rubi [A] time = 0.0141307, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {1352, 616, 31} \[ \frac{1}{7} \log \left (\frac{1}{x}+5\right )-\frac{1}{7} \log \left (\frac{2}{x}+3\right ) \]
Antiderivative was successfully verified.
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Rule 1352
Rule 616
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{\left (15+\frac{2}{x^2}+\frac{13}{x}\right ) x^2} \, dx &=-\operatorname{Subst}\left (\int \frac{1}{15+13 x+2 x^2} \, dx,x,\frac{1}{x}\right )\\ &=-\left (\frac{2}{7} \operatorname{Subst}\left (\int \frac{1}{3+2 x} \, dx,x,\frac{1}{x}\right )\right )+\frac{2}{7} \operatorname{Subst}\left (\int \frac{1}{10+2 x} \, dx,x,\frac{1}{x}\right )\\ &=\frac{1}{7} \log \left (5+\frac{1}{x}\right )-\frac{1}{7} \log \left (3+\frac{2}{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0031588, size = 21, normalized size = 0.91 \[ \frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 18, normalized size = 0.8 \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 = 1.0112, size = 23, normalized size = 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 = 1.67949, size = 50, normalized size = 2.17 \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 = 0.147482, size = 15, normalized size = 0.65 \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 = 1.09891, size = 26, normalized size = 1.13 \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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