Optimal. Leaf size=65 \[ -\frac{2187 x^5}{250}-\frac{86751 x^4}{2000}-\frac{495477 x^3}{5000}-\frac{14750667 x^2}{100000}-\frac{19846971 x}{100000}-\frac{1}{859375 (5 x+3)}-\frac{823543 \log (1-2 x)}{7744}+\frac{233 \log (5 x+3)}{9453125} \]
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Rubi [A] time = 0.0325331, antiderivative size = 65, normalized size of antiderivative = 1., 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} \[ -\frac{2187 x^5}{250}-\frac{86751 x^4}{2000}-\frac{495477 x^3}{5000}-\frac{14750667 x^2}{100000}-\frac{19846971 x}{100000}-\frac{1}{859375 (5 x+3)}-\frac{823543 \log (1-2 x)}{7744}+\frac{233 \log (5 x+3)}{9453125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^7}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac{19846971}{100000}-\frac{14750667 x}{50000}-\frac{1486431 x^2}{5000}-\frac{86751 x^3}{500}-\frac{2187 x^4}{50}-\frac{823543}{3872 (-1+2 x)}+\frac{1}{171875 (3+5 x)^2}+\frac{233}{1890625 (3+5 x)}\right ) \, dx\\ &=-\frac{19846971 x}{100000}-\frac{14750667 x^2}{100000}-\frac{495477 x^3}{5000}-\frac{86751 x^4}{2000}-\frac{2187 x^5}{250}-\frac{1}{859375 (3+5 x)}-\frac{823543 \log (1-2 x)}{7744}+\frac{233 \log (3+5 x)}{9453125}\\ \end{align*}
Mathematica [A] time = 0.0305617, size = 60, normalized size = 0.92 \[ \frac{-\frac{11 \left (9622800000 x^6+53486730000 x^5+137632770000 x^4+227660301000 x^3+315671083200 x^2-35641061775 x-99978641969\right )}{5 x+3}-257357187500 \log (1-2 x)+59648 \log (10 x+6)}{2420000000} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 50, normalized size = 0.8 \begin{align*} -{\frac{2187\,{x}^{5}}{250}}-{\frac{86751\,{x}^{4}}{2000}}-{\frac{495477\,{x}^{3}}{5000}}-{\frac{14750667\,{x}^{2}}{100000}}-{\frac{19846971\,x}{100000}}-{\frac{823543\,\ln \left ( 2\,x-1 \right ) }{7744}}-{\frac{1}{2578125+4296875\,x}}+{\frac{233\,\ln \left ( 3+5\,x \right ) }{9453125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.35074, size = 66, normalized size = 1.02 \begin{align*} -\frac{2187}{250} \, x^{5} - \frac{86751}{2000} \, x^{4} - \frac{495477}{5000} \, x^{3} - \frac{14750667}{100000} \, x^{2} - \frac{19846971}{100000} \, x - \frac{1}{859375 \,{\left (5 \, x + 3\right )}} + \frac{233}{9453125} \, \log \left (5 \, x + 3\right ) - \frac{823543}{7744} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.35881, size = 282, normalized size = 4.34 \begin{align*} -\frac{26462700000 \, x^{6} + 147088507500 \, x^{5} + 378490117500 \, x^{4} + 626065827750 \, x^{3} + 868095478800 \, x^{2} - 14912 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 64339296875 \,{\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 360222523650 \, x + 704}{605000000 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.155497, size = 58, normalized size = 0.89 \begin{align*} - \frac{2187 x^{5}}{250} - \frac{86751 x^{4}}{2000} - \frac{495477 x^{3}}{5000} - \frac{14750667 x^{2}}{100000} - \frac{19846971 x}{100000} - \frac{823543 \log{\left (x - \frac{1}{2} \right )}}{7744} + \frac{233 \log{\left (x + \frac{3}{5} \right )}}{9453125} - \frac{1}{4296875 x + 2578125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.79493, size = 122, normalized size = 1.88 \begin{align*} -\frac{27}{12500000} \,{\left (5 \, x + 3\right )}^{5}{\left (\frac{12690}{5 \, x + 3} + \frac{98100}{{\left (5 \, x + 3\right )}^{2}} + \frac{813525}{{\left (5 \, x + 3\right )}^{3}} + \frac{8951575}{{\left (5 \, x + 3\right )}^{4}} + 1296\right )} - \frac{1}{859375 \,{\left (5 \, x + 3\right )}} + \frac{531729603}{5000000} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{823543}{7744} \, \log \left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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