Optimal. Leaf size=64 \[ \frac {3897}{343 (3 x+2)}+\frac {111}{98 (3 x+2)^2}+\frac {1}{7 (3 x+2)^3}-\frac {16 \log (1-2 x)}{26411}-\frac {136419 \log (3 x+2)}{2401}+\frac {625}{11} \log (5 x+3) \]
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Rubi [A] time = 0.03, antiderivative size = 64, 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} \begin {gather*} \frac {3897}{343 (3 x+2)}+\frac {111}{98 (3 x+2)^2}+\frac {1}{7 (3 x+2)^3}-\frac {16 \log (1-2 x)}{26411}-\frac {136419 \log (3 x+2)}{2401}+\frac {625}{11} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^4 (3+5 x)} \, dx &=\int \left (-\frac {32}{26411 (-1+2 x)}-\frac {9}{7 (2+3 x)^4}-\frac {333}{49 (2+3 x)^3}-\frac {11691}{343 (2+3 x)^2}-\frac {409257}{2401 (2+3 x)}+\frac {3125}{11 (3+5 x)}\right ) \, dx\\ &=\frac {1}{7 (2+3 x)^3}+\frac {111}{98 (2+3 x)^2}+\frac {3897}{343 (2+3 x)}-\frac {16 \log (1-2 x)}{26411}-\frac {136419 \log (2+3 x)}{2401}+\frac {625}{11} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.08, size = 50, normalized size = 0.78 \begin {gather*} \frac {\frac {77 \left (70146 x^2+95859 x+32828\right )}{2 (3 x+2)^3}-16 \log (1-2 x)-1500609 \log (6 x+4)+1500625 \log (10 x+6)}{26411} \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}{(1-2 x) (2+3 x)^4 (3+5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.58, size = 98, normalized size = 1.53 \begin {gather*} \frac {5401242 \, x^{2} + 3001250 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 3001218 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 32 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (2 \, x - 1\right ) + 7381143 \, x + 2527756}{52822 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.85, size = 47, normalized size = 0.73 \begin {gather*} \frac {70146 \, x^{2} + 95859 \, x + 32828}{686 \, {\left (3 \, x + 2\right )}^{3}} + \frac {625}{11} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {136419}{2401} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {16}{26411} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 53, normalized size = 0.83 \begin {gather*} -\frac {16 \ln \left (2 x -1\right )}{26411}-\frac {136419 \ln \left (3 x +2\right )}{2401}+\frac {625 \ln \left (5 x +3\right )}{11}+\frac {1}{7 \left (3 x +2\right )^{3}}+\frac {111}{98 \left (3 x +2\right )^{2}}+\frac {3897}{343 \left (3 x +2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 54, normalized size = 0.84 \begin {gather*} \frac {70146 \, x^{2} + 95859 \, x + 32828}{686 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac {625}{11} \, \log \left (5 \, x + 3\right ) - \frac {136419}{2401} \, \log \left (3 \, x + 2\right ) - \frac {16}{26411} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 45, normalized size = 0.70 \begin {gather*} \frac {625\,\ln \left (x+\frac {3}{5}\right )}{11}-\frac {136419\,\ln \left (x+\frac {2}{3}\right )}{2401}-\frac {16\,\ln \left (x-\frac {1}{2}\right )}{26411}+\frac {\frac {1299\,x^2}{343}+\frac {10651\,x}{2058}+\frac {16414}{9261}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 56, normalized size = 0.88 \begin {gather*} - \frac {- 70146 x^{2} - 95859 x - 32828}{18522 x^{3} + 37044 x^{2} + 24696 x + 5488} - \frac {16 \log {\left (x - \frac {1}{2} \right )}}{26411} + \frac {625 \log {\left (x + \frac {3}{5} \right )}}{11} - \frac {136419 \log {\left (x + \frac {2}{3} \right )}}{2401} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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