Optimal. Leaf size=59 \[ -\frac {243 x}{200}-\frac {228095}{21296 (1-2 x)}-\frac {1}{166375 (5 x+3)}+\frac {16807}{3872 (1-2 x)^2}-\frac {1034145 \log (1-2 x)}{234256}+\frac {171 \log (5 x+3)}{1830125} \]
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Rubi [A] time = 0.03, antiderivative size = 59, 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 = {88} \begin {gather*} -\frac {243 x}{200}-\frac {228095}{21296 (1-2 x)}-\frac {1}{166375 (5 x+3)}+\frac {16807}{3872 (1-2 x)^2}-\frac {1034145 \log (1-2 x)}{234256}+\frac {171 \log (5 x+3)}{1830125} \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5}{(1-2 x)^3 (3+5 x)^2} \, dx &=\int \left (-\frac {243}{200}-\frac {16807}{968 (-1+2 x)^3}-\frac {228095}{10648 (-1+2 x)^2}-\frac {1034145}{117128 (-1+2 x)}+\frac {1}{33275 (3+5 x)^2}+\frac {171}{366025 (3+5 x)}\right ) \, dx\\ &=\frac {16807}{3872 (1-2 x)^2}-\frac {228095}{21296 (1-2 x)}-\frac {243 x}{200}-\frac {1}{166375 (3+5 x)}-\frac {1034145 \log (1-2 x)}{234256}+\frac {171 \log (3+5 x)}{1830125}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 55, normalized size = 0.93 \begin {gather*} \frac {35577630 (1-2 x)+\frac {627261250}{2 x-1}-\frac {352}{5 x+3}+\frac {254205875}{(1-2 x)^2}-258536250 \log (1-2 x)+5472 \log (10 x+6)}{58564000} \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 {(2+3 x)^5}{(1-2 x)^3 (3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.06, size = 85, normalized size = 1.44 \begin {gather*} -\frac {1423105200 \, x^{4} - 569242080 \, x^{3} - 6770697912 \, x^{2} - 5472 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 258536250 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 1684826253 \, x + 1119166477}{58564000 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 83, normalized size = 1.41 \begin {gather*} \frac {{\left (5 \, x + 3\right )} {\left (\frac {389138447}{5 \, x + 3} - \frac {1420901823}{{\left (5 \, x + 3\right )}^{2}} - 14231052\right )}}{14641000 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}^{2}} - \frac {1}{166375 \, {\left (5 \, x + 3\right )}} + \frac {8829}{2000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {1034145}{234256} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 48, normalized size = 0.81 \begin {gather*} -\frac {243 x}{200}-\frac {1034145 \ln \left (2 x -1\right )}{234256}+\frac {171 \ln \left (5 x +3\right )}{1830125}-\frac {1}{166375 \left (5 x +3\right )}+\frac {16807}{3872 \left (2 x -1\right )^{2}}+\frac {228095}{21296 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 49, normalized size = 0.83 \begin {gather*} -\frac {243}{200} \, x + \frac {570237372 \, x^{2} + 172572003 \, x - 101742407}{5324000 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac {171}{1830125} \, \log \left (5 \, x + 3\right ) - \frac {1034145}{234256} \, \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 = 0.76 \begin {gather*} \frac {171\,\ln \left (x+\frac {3}{5}\right )}{1830125}-\frac {1034145\,\ln \left (x-\frac {1}{2}\right )}{234256}-\frac {243\,x}{200}-\frac {\frac {142559343\,x^2}{26620000}+\frac {172572003\,x}{106480000}-\frac {101742407}{106480000}}{-x^3+\frac {2\,x^2}{5}+\frac {7\,x}{20}-\frac {3}{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 49, normalized size = 0.83 \begin {gather*} - \frac {243 x}{200} - \frac {- 570237372 x^{2} - 172572003 x + 101742407}{106480000 x^{3} - 42592000 x^{2} - 37268000 x + 15972000} - \frac {1034145 \log {\left (x - \frac {1}{2} \right )}}{234256} + \frac {171 \log {\left (x + \frac {3}{5} \right )}}{1830125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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