Optimal. Leaf size=53 \[ \frac {111}{49 (3 x+2)}+\frac {3}{14 (3 x+2)^2}-\frac {8 \log (1-2 x)}{3773}-\frac {3897}{343} \log (3 x+2)+\frac {125}{11} \log (5 x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 53, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {72} \[ \frac {111}{49 (3 x+2)}+\frac {3}{14 (3 x+2)^2}-\frac {8 \log (1-2 x)}{3773}-\frac {3897}{343} \log (3 x+2)+\frac {125}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx &=\int \left (-\frac {16}{3773 (-1+2 x)}-\frac {9}{7 (2+3 x)^3}-\frac {333}{49 (2+3 x)^2}-\frac {11691}{343 (2+3 x)}+\frac {625}{11 (3+5 x)}\right ) \, dx\\ &=\frac {3}{14 (2+3 x)^2}+\frac {111}{49 (2+3 x)}-\frac {8 \log (1-2 x)}{3773}-\frac {3897}{343} \log (2+3 x)+\frac {125}{11} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 49, normalized size = 0.92 \[ \frac {\frac {8547}{3 x+2}+\frac {1617}{2 (3 x+2)^2}-8 \log (1-2 x)-42867 \log (6 x+4)+42875 \log (10 x+6)}{3773} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 73, normalized size = 1.38 \[ \frac {85750 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 85734 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 16 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (2 \, x - 1\right ) + 51282 \, x + 35805}{7546 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 42, normalized size = 0.79 \[ \frac {3 \, {\left (222 \, x + 155\right )}}{98 \, {\left (3 \, x + 2\right )}^{2}} + \frac {125}{11} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {3897}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {8}{3773} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 44, normalized size = 0.83 \[ -\frac {8 \ln \left (2 x -1\right )}{3773}-\frac {3897 \ln \left (3 x +2\right )}{343}+\frac {125 \ln \left (5 x +3\right )}{11}+\frac {3}{14 \left (3 x +2\right )^{2}}+\frac {111}{49 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 44, normalized size = 0.83 \[ \frac {3 \, {\left (222 \, x + 155\right )}}{98 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac {125}{11} \, \log \left (5 \, x + 3\right ) - \frac {3897}{343} \, \log \left (3 \, x + 2\right ) - \frac {8}{3773} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 0.66 \[ \frac {125\,\ln \left (x+\frac {3}{5}\right )}{11}-\frac {3897\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {8\,\ln \left (x-\frac {1}{2}\right )}{3773}+\frac {\frac {37\,x}{49}+\frac {155}{294}}{x^2+\frac {4\,x}{3}+\frac {4}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 46, normalized size = 0.87 \[ - \frac {- 666 x - 465}{882 x^{2} + 1176 x + 392} - \frac {8 \log {\left (x - \frac {1}{2} \right )}}{3773} + \frac {125 \log {\left (x + \frac {3}{5} \right )}}{11} - \frac {3897 \log {\left (x + \frac {2}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
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