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 = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {1}{7} \log (5 x+1)-\frac {1}{7} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 616
Rule 1386
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*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} \frac {1}{7} \log (5 x+1)-\frac {1}{7} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \left (13+\frac {2}{x}+15 x\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.10, size = 17, normalized size = 0.81 \begin {gather*} \frac {1}{7} \, \log \left (5 \, x + 1\right ) - \frac {1}{7} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 19, normalized size = 0.90 \begin {gather*} \frac {1}{7} \, \log \left ({\left | 5 \, x + 1 \right |}\right ) - \frac {1}{7} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.86 \begin {gather*} \frac {\ln \left (5 x +1\right )}{7}-\frac {\ln \left (3 x +2\right )}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.93, size = 17, normalized size = 0.81 \begin {gather*} \frac {1}{7} \, \log \left (5 \, x + 1\right ) - \frac {1}{7} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 8, normalized size = 0.38 \begin {gather*} -\frac {2\,\mathrm {atanh}\left (\frac {30\,x}{7}+\frac {13}{7}\right )}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 0.71 \begin {gather*} \frac {\log {\left (x + \frac {1}{5} \right )}}{7} - \frac {\log {\left (x + \frac {2}{3} \right )}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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