Optimal. Leaf size=62 \[ -\frac {243 x^3}{250}-\frac {19683 x^2}{5000}-\frac {216999 x}{25000}-\frac {8}{75625 (5 x+3)}-\frac {1}{343750 (5 x+3)^2}-\frac {117649 \log (1-2 x)}{21296}+\frac {3347 \log (5 x+3)}{4159375} \]
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Rubi [A] time = 0.03, antiderivative size = 62, 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} \[ -\frac {243 x^3}{250}-\frac {19683 x^2}{5000}-\frac {216999 x}{25000}-\frac {8}{75625 (5 x+3)}-\frac {1}{343750 (5 x+3)^2}-\frac {117649 \log (1-2 x)}{21296}+\frac {3347 \log (5 x+3)}{4159375} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^6}{(1-2 x) (3+5 x)^3} \, dx &=\int \left (-\frac {216999}{25000}-\frac {19683 x}{2500}-\frac {729 x^2}{250}-\frac {117649}{10648 (-1+2 x)}+\frac {1}{34375 (3+5 x)^3}+\frac {8}{15125 (3+5 x)^2}+\frac {3347}{831875 (3+5 x)}\right ) \, dx\\ &=-\frac {216999 x}{25000}-\frac {19683 x^2}{5000}-\frac {243 x^3}{250}-\frac {1}{343750 (3+5 x)^2}-\frac {8}{75625 (3+5 x)}-\frac {117649 \log (1-2 x)}{21296}+\frac {3347 \log (3+5 x)}{4159375}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 56, normalized size = 0.90 \[ \frac {11 \left (-58806000 x^3-238164300 x^2-525137580 x-\frac {6400}{5 x+3}-\frac {176}{(5 x+3)^2}+329460615\right )-3676531250 \log (1-2 x)+535520 \log (10 x+6)}{665500000} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 75, normalized size = 1.21 \[ -\frac {8085825000 \, x^{5} + 42450581250 \, x^{4} + 114414423750 \, x^{3} + 98436833550 \, x^{2} - 267760 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 1838265625 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 25994486210 \, x + 106568}{332750000 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.95, size = 46, normalized size = 0.74 \[ -\frac {243}{250} \, x^{3} - \frac {19683}{5000} \, x^{2} - \frac {216999}{25000} \, x - \frac {2000 \, x + 1211}{3781250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {3347}{4159375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {117649}{21296} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 49, normalized size = 0.79 \[ -\frac {243 x^{3}}{250}-\frac {19683 x^{2}}{5000}-\frac {216999 x}{25000}-\frac {117649 \ln \left (2 x -1\right )}{21296}+\frac {3347 \ln \left (5 x +3\right )}{4159375}-\frac {1}{343750 \left (5 x +3\right )^{2}}-\frac {8}{75625 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 49, normalized size = 0.79 \[ -\frac {243}{250} \, x^{3} - \frac {19683}{5000} \, x^{2} - \frac {216999}{25000} \, x - \frac {2000 \, x + 1211}{3781250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {3347}{4159375} \, \log \left (5 \, x + 3\right ) - \frac {117649}{21296} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 43, normalized size = 0.69 \[ \frac {3347\,\ln \left (x+\frac {3}{5}\right )}{4159375}-\frac {117649\,\ln \left (x-\frac {1}{2}\right )}{21296}-\frac {216999\,x}{25000}-\frac {\frac {8\,x}{378125}+\frac {1211}{94531250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {19683\,x^2}{5000}-\frac {243\,x^3}{250} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 53, normalized size = 0.85 \[ - \frac {243 x^{3}}{250} - \frac {19683 x^{2}}{5000} - \frac {216999 x}{25000} - \frac {2000 x + 1211}{94531250 x^{2} + 113437500 x + 34031250} - \frac {117649 \log {\left (x - \frac {1}{2} \right )}}{21296} + \frac {3347 \log {\left (x + \frac {3}{5} \right )}}{4159375} \]
Verification of antiderivative is not currently implemented for this CAS.
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