Optimal. Leaf size=69 \[ \frac{30375 x^7}{28}+\frac{15525 x^6}{2}+\frac{423009 x^5}{16}+\frac{3724389 x^4}{64}+\frac{6179077 x^3}{64}+\frac{8881301 x^2}{64}+\frac{56291737 x}{256}+\frac{22370117}{512 (1-2 x)}+\frac{39220335}{256} \log (1-2 x) \]
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Rubi [A] time = 0.0363526, antiderivative size = 69, 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} \[ \frac{30375 x^7}{28}+\frac{15525 x^6}{2}+\frac{423009 x^5}{16}+\frac{3724389 x^4}{64}+\frac{6179077 x^3}{64}+\frac{8881301 x^2}{64}+\frac{56291737 x}{256}+\frac{22370117}{512 (1-2 x)}+\frac{39220335}{256} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac{56291737}{256}+\frac{8881301 x}{32}+\frac{18537231 x^2}{64}+\frac{3724389 x^3}{16}+\frac{2115045 x^4}{16}+46575 x^5+\frac{30375 x^6}{4}+\frac{22370117}{256 (-1+2 x)^2}+\frac{39220335}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{22370117}{512 (1-2 x)}+\frac{56291737 x}{256}+\frac{8881301 x^2}{64}+\frac{6179077 x^3}{64}+\frac{3724389 x^4}{64}+\frac{423009 x^5}{16}+\frac{15525 x^6}{2}+\frac{30375 x^7}{28}+\frac{39220335}{256} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.01709, size = 64, normalized size = 0.93 \[ \frac{15552000 x^8+103507200 x^7+323374464 x^6+644755104 x^5+966981680 x^4+1297354800 x^3+2157631560 x^2-3888550282 x+1098169380 (2 x-1) \log (1-2 x)+843009185}{7168 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 52, normalized size = 0.8 \begin{align*}{\frac{30375\,{x}^{7}}{28}}+{\frac{15525\,{x}^{6}}{2}}+{\frac{423009\,{x}^{5}}{16}}+{\frac{3724389\,{x}^{4}}{64}}+{\frac{6179077\,{x}^{3}}{64}}+{\frac{8881301\,{x}^{2}}{64}}+{\frac{56291737\,x}{256}}+{\frac{39220335\,\ln \left ( 2\,x-1 \right ) }{256}}-{\frac{22370117}{1024\,x-512}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05036, size = 69, normalized size = 1. \begin{align*} \frac{30375}{28} \, x^{7} + \frac{15525}{2} \, x^{6} + \frac{423009}{16} \, x^{5} + \frac{3724389}{64} \, x^{4} + \frac{6179077}{64} \, x^{3} + \frac{8881301}{64} \, x^{2} + \frac{56291737}{256} \, x - \frac{22370117}{512 \,{\left (2 \, x - 1\right )}} + \frac{39220335}{256} \, \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 = 1.19342, size = 255, normalized size = 3.7 \begin{align*} \frac{7776000 \, x^{8} + 51753600 \, x^{7} + 161687232 \, x^{6} + 322377552 \, x^{5} + 483490840 \, x^{4} + 648677400 \, x^{3} + 1078815780 \, x^{2} + 549084690 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 788084318 \, x - 156590819}{3584 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.118988, size = 61, normalized size = 0.88 \begin{align*} \frac{30375 x^{7}}{28} + \frac{15525 x^{6}}{2} + \frac{423009 x^{5}}{16} + \frac{3724389 x^{4}}{64} + \frac{6179077 x^{3}}{64} + \frac{8881301 x^{2}}{64} + \frac{56291737 x}{256} + \frac{39220335 \log{\left (2 x - 1 \right )}}{256} - \frac{22370117}{1024 x - 512} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.65865, size = 126, normalized size = 1.83 \begin{align*} \frac{1}{7168} \,{\left (2 \, x - 1\right )}^{7}{\left (\frac{1294650}{2 \, x - 1} + \frac{12414276}{{\left (2 \, x - 1\right )}^{2}} + \frac{70848603}{{\left (2 \, x - 1\right )}^{3}} + \frac{269525480}{{\left (2 \, x - 1\right )}^{4}} + \frac{738160010}{{\left (2 \, x - 1\right )}^{5}} + \frac{1684493580}{{\left (2 \, x - 1\right )}^{6}} + 60750\right )} - \frac{22370117}{512 \,{\left (2 \, x - 1\right )}} - \frac{39220335}{256} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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