Optimal. Leaf size=47 \[ -\frac {243 x^4}{40}-\frac {2619 x^3}{100}-\frac {107433 x^2}{2000}-\frac {848277 x}{10000}-\frac {16807}{352} \log (1-2 x)+\frac {\log (5 x+3)}{34375} \]
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Rubi [A] time = 0.02, antiderivative size = 47, 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 {243 x^4}{40}-\frac {2619 x^3}{100}-\frac {107433 x^2}{2000}-\frac {848277 x}{10000}-\frac {16807}{352} \log (1-2 x)+\frac {\log (5 x+3)}{34375} \end {gather*}
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac {848277}{10000}-\frac {107433 x}{1000}-\frac {7857 x^2}{100}-\frac {243 x^3}{10}-\frac {16807}{176 (-1+2 x)}+\frac {1}{6875 (3+5 x)}\right ) \, dx\\ &=-\frac {848277 x}{10000}-\frac {107433 x^2}{2000}-\frac {2619 x^3}{100}-\frac {243 x^4}{40}-\frac {16807}{352} \log (1-2 x)+\frac {\log (3+5 x)}{34375}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 45, normalized size = 0.96 \begin {gather*} \frac {-110 \left (60750 x^4+261900 x^3+537165 x^2+848277 x+392378\right )-52521875 \log (3-6 x)+32 \log (-3 (5 x+3))}{1100000} \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+5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.40, size = 35, normalized size = 0.74 \begin {gather*} -\frac {243}{40} \, x^{4} - \frac {2619}{100} \, x^{3} - \frac {107433}{2000} \, x^{2} - \frac {848277}{10000} \, x + \frac {1}{34375} \, \log \left (5 \, x + 3\right ) - \frac {16807}{352} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 37, normalized size = 0.79 \begin {gather*} -\frac {243}{40} \, x^{4} - \frac {2619}{100} \, x^{3} - \frac {107433}{2000} \, x^{2} - \frac {848277}{10000} \, x + \frac {1}{34375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {16807}{352} \, \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 = 0.00, size = 36, normalized size = 0.77 \begin {gather*} -\frac {243 x^{4}}{40}-\frac {2619 x^{3}}{100}-\frac {107433 x^{2}}{2000}-\frac {848277 x}{10000}-\frac {16807 \ln \left (2 x -1\right )}{352}+\frac {\ln \left (5 x +3\right )}{34375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 35, normalized size = 0.74 \begin {gather*} -\frac {243}{40} \, x^{4} - \frac {2619}{100} \, x^{3} - \frac {107433}{2000} \, x^{2} - \frac {848277}{10000} \, x + \frac {1}{34375} \, \log \left (5 \, x + 3\right ) - \frac {16807}{352} \, \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 = 1.12, size = 31, normalized size = 0.66 \begin {gather*} \frac {\ln \left (x+\frac {3}{5}\right )}{34375}-\frac {16807\,\ln \left (x-\frac {1}{2}\right )}{352}-\frac {848277\,x}{10000}-\frac {107433\,x^2}{2000}-\frac {2619\,x^3}{100}-\frac {243\,x^4}{40} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 42, normalized size = 0.89 \begin {gather*} - \frac {243 x^{4}}{40} - \frac {2619 x^{3}}{100} - \frac {107433 x^{2}}{2000} - \frac {848277 x}{10000} - \frac {16807 \log {\left (x - \frac {1}{2} \right )}}{352} + \frac {\log {\left (x + \frac {3}{5} \right )}}{34375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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