Optimal. Leaf size=73 \[ -\frac{729 x^3}{200}-\frac{108621 x^2}{4000}-\frac{1258983 x}{10000}-\frac{18941489}{85184 (1-2 x)}-\frac{1}{4159375 (5 x+3)}+\frac{823543}{15488 (1-2 x)^2}-\frac{87177909 \log (1-2 x)}{468512}+\frac{237 \log (5 x+3)}{45753125} \]
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Rubi [A] time = 0.0396953, antiderivative size = 73, 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} \[ -\frac{729 x^3}{200}-\frac{108621 x^2}{4000}-\frac{1258983 x}{10000}-\frac{18941489}{85184 (1-2 x)}-\frac{1}{4159375 (5 x+3)}+\frac{823543}{15488 (1-2 x)^2}-\frac{87177909 \log (1-2 x)}{468512}+\frac{237 \log (5 x+3)}{45753125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^7}{(1-2 x)^3 (3+5 x)^2} \, dx &=\int \left (-\frac{1258983}{10000}-\frac{108621 x}{2000}-\frac{2187 x^2}{200}-\frac{823543}{3872 (-1+2 x)^3}-\frac{18941489}{42592 (-1+2 x)^2}-\frac{87177909}{234256 (-1+2 x)}+\frac{1}{831875 (3+5 x)^2}+\frac{237}{9150625 (3+5 x)}\right ) \, dx\\ &=\frac{823543}{15488 (1-2 x)^2}-\frac{18941489}{85184 (1-2 x)}-\frac{1258983 x}{10000}-\frac{108621 x^2}{4000}-\frac{729 x^3}{200}-\frac{1}{4159375 (3+5 x)}-\frac{87177909 \log (1-2 x)}{468512}+\frac{237 \log (3+5 x)}{45753125}\\ \end{align*}
Mathematica [A] time = 0.0439183, size = 67, normalized size = 0.92 \[ \frac{-\frac{22 \left (4851495000 x^6+34203039750 x^5+151415158950 x^4-172378468845 x^3-163837494156 x^2+25343933346 x+19763981131\right )}{(1-2 x)^2 (5 x+3)}-272430965625 \log (1-2 x)+7584 \log (10 x+6)}{1464100000} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 58, normalized size = 0.8 \begin{align*} -{\frac{729\,{x}^{3}}{200}}-{\frac{108621\,{x}^{2}}{4000}}-{\frac{1258983\,x}{10000}}+{\frac{823543}{15488\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{18941489}{170368\,x-85184}}-{\frac{87177909\,\ln \left ( 2\,x-1 \right ) }{468512}}-{\frac{1}{12478125+20796875\,x}}+{\frac{237\,\ln \left ( 3+5\,x \right ) }{45753125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02032, size = 80, normalized size = 1.1 \begin{align*} -\frac{729}{200} \, x^{3} - \frac{108621}{4000} \, x^{2} - \frac{1258983}{10000} \, x + \frac{1183843061988 \, x^{2} + 259930759887 \, x - 270225047003}{532400000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{237}{45753125} \, \log \left (5 \, x + 3\right ) - \frac{87177909}{468512} \, \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 = 1.41234, size = 378, normalized size = 5.18 \begin{align*} -\frac{426931560000 \, x^{6} + 3009867498000 \, x^{5} + 13324533987600 \, x^{4} - 6947670741660 \, x^{3} - 17706353292408 \, x^{2} - 30336 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 1089723862500 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 647305946397 \, x + 2972475517033}{5856400000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.194951, size = 63, normalized size = 0.86 \begin{align*} - \frac{729 x^{3}}{200} - \frac{108621 x^{2}}{4000} - \frac{1258983 x}{10000} + \frac{1183843061988 x^{2} + 259930759887 x - 270225047003}{10648000000 x^{3} - 4259200000 x^{2} - 3726800000 x + 1597200000} - \frac{87177909 \log{\left (x - \frac{1}{2} \right )}}{468512} + \frac{237 \log{\left (x + \frac{3}{5} \right )}}{45753125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.01243, size = 139, normalized size = 1.9 \begin{align*} -\frac{{\left (5 \, x + 3\right )}^{3}{\left (\frac{1472913882}{5 \, x + 3} + \frac{33001809588}{{\left (5 \, x + 3\right )}^{2}} - \frac{817302548083}{{\left (5 \, x + 3\right )}^{3}} + \frac{2996736348771}{{\left (5 \, x + 3\right )}^{4}} + 85386312\right )}}{732050000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{1}{4159375 \,{\left (5 \, x + 3\right )}} + \frac{18607401}{100000} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{87177909}{468512} \, \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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