Optimal. Leaf size=55 \[ \frac {243 x^2}{200}+\frac {3807 x}{500}+\frac {16807}{1936 (1-2 x)}-\frac {1}{75625 (5 x+3)}+\frac {228095 \log (1-2 x)}{21296}+\frac {169 \log (5 x+3)}{831875} \]
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Rubi [A] time = 0.03, antiderivative size = 55, 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} \[ \frac {243 x^2}{200}+\frac {3807 x}{500}+\frac {16807}{1936 (1-2 x)}-\frac {1}{75625 (5 x+3)}+\frac {228095 \log (1-2 x)}{21296}+\frac {169 \log (5 x+3)}{831875} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5}{(1-2 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac {3807}{500}+\frac {243 x}{100}+\frac {16807}{968 (-1+2 x)^2}+\frac {228095}{10648 (-1+2 x)}+\frac {1}{15125 (3+5 x)^2}+\frac {169}{166375 (3+5 x)}\right ) \, dx\\ &=\frac {16807}{1936 (1-2 x)}+\frac {3807 x}{500}+\frac {243 x^2}{200}-\frac {1}{75625 (3+5 x)}+\frac {228095 \log (1-2 x)}{21296}+\frac {169 \log (3+5 x)}{831875}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 56, normalized size = 1.02 \[ \frac {-\frac {11 (52521907 x+31513109)}{10 x^2+x-3}+1796850 (3 x+2)^2+26593380 (3 x+2)+142559375 \log (3-6 x)+2704 \log (-3 (5 x+3))}{13310000} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 64, normalized size = 1.16 \[ \frac {161716500 \, x^{4} + 1029595050 \, x^{3} + 52827390 \, x^{2} + 2704 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 142559375 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 881767997 \, x - 346644199}{13310000 \, {\left (10 \, x^{2} + x - 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.23, size = 85, normalized size = 1.55 \[ -\frac {{\left (5 \, x + 3\right )}^{2} {\left (\frac {12829509}{5 \, x + 3} - \frac {142651871}{{\left (5 \, x + 3\right )}^{2}} + 646866\right )}}{6655000 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}} - \frac {1}{75625 \, {\left (5 \, x + 3\right )}} - \frac {107109}{10000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) + \frac {228095}{21296} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 44, normalized size = 0.80 \[ \frac {243 x^{2}}{200}+\frac {3807 x}{500}+\frac {228095 \ln \left (2 x -1\right )}{21296}+\frac {169 \ln \left (5 x +3\right )}{831875}-\frac {1}{75625 \left (5 x +3\right )}-\frac {16807}{1936 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 42, normalized size = 0.76 \[ \frac {243}{200} \, x^{2} + \frac {3807}{500} \, x - \frac {52521907 \, x + 31513109}{1210000 \, {\left (10 \, x^{2} + x - 3\right )}} + \frac {169}{831875} \, \log \left (5 \, x + 3\right ) + \frac {228095}{21296} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 38, normalized size = 0.69 \[ \frac {3807\,x}{500}+\frac {228095\,\ln \left (x-\frac {1}{2}\right )}{21296}+\frac {169\,\ln \left (x+\frac {3}{5}\right )}{831875}-\frac {\frac {52521907\,x}{12100000}+\frac {31513109}{12100000}}{x^2+\frac {x}{10}-\frac {3}{10}}+\frac {243\,x^2}{200} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 48, normalized size = 0.87 \[ \frac {243 x^{2}}{200} + \frac {3807 x}{500} + \frac {- 52521907 x - 31513109}{12100000 x^{2} + 1210000 x - 3630000} + \frac {228095 \log {\left (x - \frac {1}{2} \right )}}{21296} + \frac {169 \log {\left (x + \frac {3}{5} \right )}}{831875} \]
Verification of antiderivative is not currently implemented for this CAS.
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