Optimal. Leaf size=62 \[ -\frac {216999 x}{25000}-\frac {19683 x^2}{5000}-\frac {243 x^3}{250}-\frac {1}{343750 (3+5 x)^2}-\frac {8}{75625 (3+5 x)}-\frac {117649 \log (1-2 x)}{21296}+\frac {3347 \log (3+5 x)}{4159375} \]
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Rubi [A]
time = 0.02, 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 = {90}
\begin {gather*} -\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} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
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 = 0.03, size = 56, normalized size = 0.90 \begin {gather*} \frac {11 \left (329460615-525137580 x-238164300 x^2-58806000 x^3-\frac {176}{(3+5 x)^2}-\frac {6400}{3+5 x}\right )-3676531250 \log (1-2 x)+535520 \log (6+10 x)}{665500000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 49, normalized size = 0.79
method | result | size |
risch | \(-\frac {243 x^{3}}{250}-\frac {19683 x^{2}}{5000}-\frac {216999 x}{25000}+\frac {-\frac {8 x}{15125}-\frac {1211}{3781250}}{\left (3+5 x \right )^{2}}-\frac {117649 \ln \left (-1+2 x \right )}{21296}+\frac {3347 \ln \left (3+5 x \right )}{4159375}\) | \(45\) |
default | \(-\frac {243 x^{3}}{250}-\frac {19683 x^{2}}{5000}-\frac {216999 x}{25000}-\frac {117649 \ln \left (-1+2 x \right )}{21296}-\frac {1}{343750 \left (3+5 x \right )^{2}}-\frac {8}{75625 \left (3+5 x \right )}+\frac {3347 \ln \left (3+5 x \right )}{4159375}\) | \(49\) |
norman | \(\frac {-\frac {141786169}{1815000} x -\frac {322155941}{1089000} x^{2}-\frac {68769}{200} x^{3}-\frac {5103}{40} x^{4}-\frac {243}{10} x^{5}}{\left (3+5 x \right )^{2}}-\frac {117649 \ln \left (-1+2 x \right )}{21296}+\frac {3347 \ln \left (3+5 x \right )}{4159375}\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 49, normalized size = 0.79 \begin {gather*} -\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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.93, size = 75, normalized size = 1.21 \begin {gather*} -\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 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 53, normalized size = 0.85 \begin {gather*} - \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.68, size = 46, normalized size = 0.74 \begin {gather*} -\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 ) \end {gather*}
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 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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