Optimal. Leaf size=65 \[ \frac {2187 x^5}{100}+\frac {13851 x^4}{100}+\frac {853659 x^3}{2000}+\frac {18237069 x^2}{20000}+\frac {370109547 x}{200000}+\frac {823543}{1408 (1-2 x)}+\frac {5764801 \log (1-2 x)}{3872}+\frac {\log (5 x+3)}{1890625} \]
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Rubi [A] time = 0.03, antiderivative size = 65, 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} \[ \frac {2187 x^5}{100}+\frac {13851 x^4}{100}+\frac {853659 x^3}{2000}+\frac {18237069 x^2}{20000}+\frac {370109547 x}{200000}+\frac {823543}{1408 (1-2 x)}+\frac {5764801 \log (1-2 x)}{3872}+\frac {\log (5 x+3)}{1890625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac {370109547}{200000}+\frac {18237069 x}{10000}+\frac {2560977 x^2}{2000}+\frac {13851 x^3}{25}+\frac {2187 x^4}{20}+\frac {823543}{704 (-1+2 x)^2}+\frac {5764801}{1936 (-1+2 x)}+\frac {1}{378125 (3+5 x)}\right ) \, dx\\ &=\frac {823543}{1408 (1-2 x)}+\frac {370109547 x}{200000}+\frac {18237069 x^2}{20000}+\frac {853659 x^3}{2000}+\frac {13851 x^4}{100}+\frac {2187 x^5}{100}+\frac {5764801 \log (1-2 x)}{3872}+\frac {\log (3+5 x)}{1890625}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 60, normalized size = 0.92 \[ \frac {\frac {11 \left (4811400000 x^6+28066500000 x^5+78666390000 x^4+153656514000 x^3+306816622200 x^2-14798867886 x-158719988357\right )}{2 x-1}+1801500312500 \log (5-10 x)+640 \log (5 x+3)}{1210000000} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 65, normalized size = 1.00 \[ \frac {10585080000 \, x^{6} + 61746300000 \, x^{5} + 173066058000 \, x^{4} + 338044330800 \, x^{3} + 674996568840 \, x^{2} + 128 \, {\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 360300062500 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 447832551870 \, x - 141546453125}{242000000 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.03, size = 90, normalized size = 1.38 \[ \frac {27}{400000} \, {\left (2 \, x - 1\right )}^{5} {\left (\frac {178875}{2 \, x - 1} + \frac {1404675}{{\left (2 \, x - 1\right )}^{2}} + \frac {6619260}{{\left (2 \, x - 1\right )}^{3}} + \frac {23397131}{{\left (2 \, x - 1\right )}^{4}} + 10125\right )} - \frac {823543}{1408 \, {\left (2 \, x - 1\right )}} - \frac {744421617}{500000} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {1}{1890625} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 50, normalized size = 0.77 \[ \frac {2187 x^{5}}{100}+\frac {13851 x^{4}}{100}+\frac {853659 x^{3}}{2000}+\frac {18237069 x^{2}}{20000}+\frac {370109547 x}{200000}+\frac {5764801 \ln \left (2 x -1\right )}{3872}+\frac {\ln \left (5 x +3\right )}{1890625}-\frac {823543}{1408 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 49, normalized size = 0.75 \[ \frac {2187}{100} \, x^{5} + \frac {13851}{100} \, x^{4} + \frac {853659}{2000} \, x^{3} + \frac {18237069}{20000} \, x^{2} + \frac {370109547}{200000} \, x - \frac {823543}{1408 \, {\left (2 \, x - 1\right )}} + \frac {1}{1890625} \, \log \left (5 \, x + 3\right ) + \frac {5764801}{3872} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.08, size = 45, normalized size = 0.69 \[ \frac {370109547\,x}{200000}+\frac {5764801\,\ln \left (x-\frac {1}{2}\right )}{3872}+\frac {\ln \left (x+\frac {3}{5}\right )}{1890625}-\frac {823543}{2816\,\left (x-\frac {1}{2}\right )}+\frac {18237069\,x^2}{20000}+\frac {853659\,x^3}{2000}+\frac {13851\,x^4}{100}+\frac {2187\,x^5}{100} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 56, normalized size = 0.86 \[ \frac {2187 x^{5}}{100} + \frac {13851 x^{4}}{100} + \frac {853659 x^{3}}{2000} + \frac {18237069 x^{2}}{20000} + \frac {370109547 x}{200000} + \frac {5764801 \log {\left (x - \frac {1}{2} \right )}}{3872} + \frac {\log {\left (x + \frac {3}{5} \right )}}{1890625} - \frac {823543}{2816 x - 1408} \]
Verification of antiderivative is not currently implemented for this CAS.
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