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 = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, 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 31
Rule 616
Rule 1352
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*}
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Mathematica [A] time = 0.00, 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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fricas [A] time = 1.01, size = 17, normalized size = 0.74 \[ \frac {1}{7} \, \log \left (5 \, x + 1\right ) - \frac {1}{7} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 19, normalized size = 0.83 \[ \frac {1}{7} \, \log \left ({\left | 5 \, x + 1 \right |}\right ) - \frac {1}{7} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 18, normalized size = 0.78 \[ \frac {\ln \left (5 x +1\right )}{7}-\frac {\ln \left (3 x +2\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 17, normalized size = 0.74 \[ \frac {1}{7} \, \log \left (5 \, x + 1\right ) - \frac {1}{7} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.37, size = 8, normalized size = 0.35 \[ -\frac {2\,\mathrm {atanh}\left (\frac {30\,x}{7}+\frac {13}{7}\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 0.65 \[ \frac {\log {\left (x + \frac {1}{5} \right )}}{7} - \frac {\log {\left (x + \frac {2}{3} \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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