Optimal. Leaf size=51 \[ -\frac {69039 x}{5000}-\frac {6399 x^2}{1000}-\frac {81 x^3}{50}-\frac {1}{34375 (3+5 x)}-\frac {16807 \log (1-2 x)}{1936}+\frac {167 \log (3+5 x)}{378125} \]
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Rubi [A]
time = 0.01, antiderivative size = 51, 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 {81 x^3}{50}-\frac {6399 x^2}{1000}-\frac {69039 x}{5000}-\frac {1}{34375 (5 x+3)}-\frac {16807 \log (1-2 x)}{1936}+\frac {167 \log (5 x+3)}{378125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac {69039}{5000}-\frac {6399 x}{500}-\frac {243 x^2}{50}-\frac {16807}{968 (-1+2 x)}+\frac {1}{6875 (3+5 x)^2}+\frac {167}{75625 (3+5 x)}\right ) \, dx\\ &=-\frac {69039 x}{5000}-\frac {6399 x^2}{1000}-\frac {81 x^3}{50}-\frac {1}{34375 (3+5 x)}-\frac {16807 \log (1-2 x)}{1936}+\frac {167 \log (3+5 x)}{378125}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 50, normalized size = 0.98 \begin {gather*} \frac {-\frac {11 \left (-28730263-2318085 x+97059600 x^2+40540500 x^3+8910000 x^4\right )}{3+5 x}-105043750 \log (1-2 x)+5344 \log (6+10 x)}{12100000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 40, normalized size = 0.78
method | result | size |
risch | \(-\frac {81 x^{3}}{50}-\frac {6399 x^{2}}{1000}-\frac {69039 x}{5000}-\frac {1}{171875 \left (x +\frac {3}{5}\right )}-\frac {16807 \ln \left (-1+2 x \right )}{1936}+\frac {167 \ln \left (3+5 x \right )}{378125}\) | \(38\) |
default | \(-\frac {81 x^{3}}{50}-\frac {6399 x^{2}}{1000}-\frac {69039 x}{5000}-\frac {16807 \ln \left (-1+2 x \right )}{1936}-\frac {1}{34375 \left (3+5 x \right )}+\frac {167 \ln \left (3+5 x \right )}{378125}\) | \(40\) |
norman | \(\frac {-\frac {6834853}{165000} x -\frac {22059}{250} x^{2}-\frac {7371}{200} x^{3}-\frac {81}{10} x^{4}}{3+5 x}-\frac {16807 \ln \left (-1+2 x \right )}{1936}+\frac {167 \ln \left (3+5 x \right )}{378125}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 39, normalized size = 0.76 \begin {gather*} -\frac {81}{50} \, x^{3} - \frac {6399}{1000} \, x^{2} - \frac {69039}{5000} \, x - \frac {1}{34375 \, {\left (5 \, x + 3\right )}} + \frac {167}{378125} \, \log \left (5 \, x + 3\right ) - \frac {16807}{1936} \, \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 = 0.91, size = 55, normalized size = 1.08 \begin {gather*} -\frac {49005000 \, x^{4} + 222972750 \, x^{3} + 533827800 \, x^{2} - 2672 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 52521875 \, {\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 250611570 \, x + 176}{6050000 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 44, normalized size = 0.86 \begin {gather*} - \frac {81 x^{3}}{50} - \frac {6399 x^{2}}{1000} - \frac {69039 x}{5000} - \frac {16807 \log {\left (x - \frac {1}{2} \right )}}{1936} + \frac {167 \log {\left (x + \frac {3}{5} \right )}}{378125} - \frac {1}{171875 x + 103125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.03, size = 72, normalized size = 1.41 \begin {gather*} -\frac {27}{25000} \, {\left (5 \, x + 3\right )}^{3} {\left (\frac {129}{5 \, x + 3} + \frac {1459}{{\left (5 \, x + 3\right )}^{2}} + 12\right )} - \frac {1}{34375 \, {\left (5 \, x + 3\right )}} + \frac {434043}{50000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {16807}{1936} \, \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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Mupad [B]
time = 0.04, size = 35, normalized size = 0.69 \begin {gather*} \frac {167\,\ln \left (x+\frac {3}{5}\right )}{378125}-\frac {16807\,\ln \left (x-\frac {1}{2}\right )}{1936}-\frac {69039\,x}{5000}-\frac {1}{171875\,\left (x+\frac {3}{5}\right )}-\frac {6399\,x^2}{1000}-\frac {81\,x^3}{50} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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