Optimal. Leaf size=41 \[ -\frac {1}{4 x^2}+\frac {13}{4 x}+\frac {139 \log (x)}{8}+\frac {27}{56} \log (3 x+2)-\frac {125}{7} \log (5 x+1) \]
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Rubi [A] time = 0.03, antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {1585, 709, 800} \[ -\frac {1}{4 x^2}+\frac {13}{4 x}+\frac {139 \log (x)}{8}+\frac {27}{56} \log (3 x+2)-\frac {125}{7} \log (5 x+1) \]
Antiderivative was successfully verified.
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Rule 709
Rule 800
Rule 1585
Rubi steps
\begin {align*} \int \frac {1}{x^2 \left (2 x+13 x^2+15 x^3\right )} \, dx &=\int \frac {1}{x^3 \left (2+13 x+15 x^2\right )} \, dx\\ &=-\frac {1}{4 x^2}+\frac {1}{2} \int \frac {-13-15 x}{x^2 \left (2+13 x+15 x^2\right )} \, dx\\ &=-\frac {1}{4 x^2}+\frac {1}{2} \int \left (-\frac {13}{2 x^2}+\frac {139}{4 x}+\frac {81}{28 (2+3 x)}-\frac {1250}{7 (1+5 x)}\right ) \, dx\\ &=-\frac {1}{4 x^2}+\frac {13}{4 x}+\frac {139 \log (x)}{8}+\frac {27}{56} \log (2+3 x)-\frac {125}{7} \log (1+5 x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 41, normalized size = 1.00 \[ -\frac {1}{4 x^2}+\frac {13}{4 x}+\frac {139 \log (x)}{8}+\frac {27}{56} \log (3 x+2)-\frac {125}{7} \log (5 x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.15, size = 39, normalized size = 0.95 \[ -\frac {1000 \, x^{2} \log \left (5 \, x + 1\right ) - 27 \, x^{2} \log \left (3 \, x + 2\right ) - 973 \, x^{2} \log \relax (x) - 182 \, x + 14}{56 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 34, normalized size = 0.83 \[ \frac {13 \, x - 1}{4 \, x^{2}} - \frac {125}{7} \, \log \left ({\left | 5 \, x + 1 \right |}\right ) + \frac {27}{56} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {139}{8} \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 32, normalized size = 0.78 \[ \frac {139 \ln \relax (x )}{8}-\frac {125 \ln \left (5 x +1\right )}{7}+\frac {27 \ln \left (3 x +2\right )}{56}+\frac {13}{4 x}-\frac {1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 31, normalized size = 0.76 \[ \frac {13 \, x - 1}{4 \, x^{2}} - \frac {125}{7} \, \log \left (5 \, x + 1\right ) + \frac {27}{56} \, \log \left (3 \, x + 2\right ) + \frac {139}{8} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 26, normalized size = 0.63 \[ \frac {27\,\ln \left (x+\frac {2}{3}\right )}{56}-\frac {125\,\ln \left (x+\frac {1}{5}\right )}{7}+\frac {139\,\ln \relax (x)}{8}+\frac {\frac {13\,x}{4}-\frac {1}{4}}{x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 36, normalized size = 0.88 \[ \frac {139 \log {\relax (x )}}{8} - \frac {125 \log {\left (x + \frac {1}{5} \right )}}{7} + \frac {27 \log {\left (x + \frac {2}{3} \right )}}{56} + \frac {13 x - 1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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