Optimal. Leaf size=76 \[ -\frac{6561 x^5}{200}-\frac{408969 x^4}{1600}-\frac{124416 x^3}{125}-\frac{110180817 x^2}{40000}-\frac{2941619571 x}{400000}-\frac{188591347}{30976 (1-2 x)}+\frac{5764801}{5632 (1-2 x)^2}-\frac{2644396573 \log (1-2 x)}{340736}+\frac{\log (5 x+3)}{20796875} \]
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Rubi [A] time = 0.0385941, antiderivative size = 76, 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} \[ -\frac{6561 x^5}{200}-\frac{408969 x^4}{1600}-\frac{124416 x^3}{125}-\frac{110180817 x^2}{40000}-\frac{2941619571 x}{400000}-\frac{188591347}{30976 (1-2 x)}+\frac{5764801}{5632 (1-2 x)^2}-\frac{2644396573 \log (1-2 x)}{340736}+\frac{\log (5 x+3)}{20796875} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^8}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac{2941619571}{400000}-\frac{110180817 x}{20000}-\frac{373248 x^2}{125}-\frac{408969 x^3}{400}-\frac{6561 x^4}{40}-\frac{5764801}{1408 (-1+2 x)^3}-\frac{188591347}{15488 (-1+2 x)^2}-\frac{2644396573}{170368 (-1+2 x)}+\frac{1}{4159375 (3+5 x)}\right ) \, dx\\ &=\frac{5764801}{5632 (1-2 x)^2}-\frac{188591347}{30976 (1-2 x)}-\frac{2941619571 x}{400000}-\frac{110180817 x^2}{40000}-\frac{124416 x^3}{125}-\frac{408969 x^4}{1600}-\frac{6561 x^5}{200}-\frac{2644396573 \log (1-2 x)}{340736}+\frac{\log (3+5 x)}{20796875}\\ \end{align*}
Mathematica [A] time = 0.0421093, size = 98, normalized size = 1.29 \[ -\frac{27}{200} (3 x+2)^5-\frac{2889 (3 x+2)^4}{1600}-\frac{17019 (3 x+2)^3}{1000}-\frac{5992353 (3 x+2)^2}{40000}-\frac{631722537 (3 x+2)}{400000}+\frac{188591347}{30976 (2 x-1)}+\frac{5764801}{5632 (1-2 x)^2}-\frac{2644396573 \log (3-6 x)}{340736}+\frac{\log (-3 (5 x+3))}{20796875} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 59, normalized size = 0.8 \begin{align*} -{\frac{6561\,{x}^{5}}{200}}-{\frac{408969\,{x}^{4}}{1600}}-{\frac{124416\,{x}^{3}}{125}}-{\frac{110180817\,{x}^{2}}{40000}}-{\frac{2941619571\,x}{400000}}+{\frac{5764801}{5632\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{188591347}{61952\,x-30976}}-{\frac{2644396573\,\ln \left ( 2\,x-1 \right ) }{340736}}+{\frac{\ln \left ( 3+5\,x \right ) }{20796875}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06654, size = 80, normalized size = 1.05 \begin{align*} -\frac{6561}{200} \, x^{5} - \frac{408969}{1600} \, x^{4} - \frac{124416}{125} \, x^{3} - \frac{110180817}{40000} \, x^{2} - \frac{2941619571}{400000} \, x + \frac{823543 \,{\left (916 \, x - 381\right )}}{61952 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{1}{20796875} \, \log \left (5 \, x + 3\right ) - \frac{2644396573}{340736} \, \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 = 1.63589, size = 379, normalized size = 4.99 \begin{align*} -\frac{1397230560000 \, x^{7} + 9489524220000 \, x^{6} + 31855563036000 \, x^{5} + 77649212460600 \, x^{4} + 206501370522480 \, x^{3} - 283893518434680 \, x^{2} - 512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) + 82637392906250 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 51350638082480 \, x + 53929198640625}{10648000000 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.174255, size = 65, normalized size = 0.86 \begin{align*} - \frac{6561 x^{5}}{200} - \frac{408969 x^{4}}{1600} - \frac{124416 x^{3}}{125} - \frac{110180817 x^{2}}{40000} - \frac{2941619571 x}{400000} + \frac{754365388 x - 313769883}{247808 x^{2} - 247808 x + 61952} - \frac{2644396573 \log{\left (x - \frac{1}{2} \right )}}{340736} + \frac{\log{\left (x + \frac{3}{5} \right )}}{20796875} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.80905, size = 76, normalized size = 1. \begin{align*} -\frac{6561}{200} \, x^{5} - \frac{408969}{1600} \, x^{4} - \frac{124416}{125} \, x^{3} - \frac{110180817}{40000} \, x^{2} - \frac{2941619571}{400000} \, x + \frac{823543 \,{\left (916 \, x - 381\right )}}{61952 \,{\left (2 \, x - 1\right )}^{2}} + \frac{1}{20796875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{2644396573}{340736} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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