Optimal. Leaf size=62 \[ -\frac{243 x^3}{40}-\frac{35721 x^2}{800}-\frac{102303 x}{500}-\frac{2739541}{7744 (1-2 x)}+\frac{117649}{1408 (1-2 x)^2}-\frac{12761315 \log (1-2 x)}{42592}+\frac{\log (5 x+3)}{831875} \]
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Rubi [A] time = 0.0296764, antiderivative size = 62, 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} \[ -\frac{243 x^3}{40}-\frac{35721 x^2}{800}-\frac{102303 x}{500}-\frac{2739541}{7744 (1-2 x)}+\frac{117649}{1408 (1-2 x)^2}-\frac{12761315 \log (1-2 x)}{42592}+\frac{\log (5 x+3)}{831875} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^6}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac{102303}{500}-\frac{35721 x}{400}-\frac{729 x^2}{40}-\frac{117649}{352 (-1+2 x)^3}-\frac{2739541}{3872 (-1+2 x)^2}-\frac{12761315}{21296 (-1+2 x)}+\frac{1}{166375 (3+5 x)}\right ) \, dx\\ &=\frac{117649}{1408 (1-2 x)^2}-\frac{2739541}{7744 (1-2 x)}-\frac{102303 x}{500}-\frac{35721 x^2}{800}-\frac{243 x^3}{40}-\frac{12761315 \log (1-2 x)}{42592}+\frac{\log (3+5 x)}{831875}\\ \end{align*}
Mathematica [A] time = 0.0277894, size = 55, normalized size = 0.89 \[ \frac{-\frac{11 \left (235224000 x^5+1493672400 x^4+6252253920 x^3-3308307948 x^2-9050078692 x+3661042443\right )}{(1-2 x)^2}-31903287500 \log (5-10 x)+128 \log (5 x+3)}{106480000} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 49, normalized size = 0.8 \begin{align*} -{\frac{243\,{x}^{3}}{40}}-{\frac{35721\,{x}^{2}}{800}}-{\frac{102303\,x}{500}}+{\frac{117649}{1408\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{2739541}{15488\,x-7744}}-{\frac{12761315\,\ln \left ( 2\,x-1 \right ) }{42592}}+{\frac{\ln \left ( 3+5\,x \right ) }{831875}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.48885, size = 66, normalized size = 1.06 \begin{align*} -\frac{243}{40} \, x^{3} - \frac{35721}{800} \, x^{2} - \frac{102303}{500} \, x + \frac{16807 \,{\left (652 \, x - 249\right )}}{15488 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{1}{831875} \, \log \left (5 \, x + 3\right ) - \frac{12761315}{42592} \, \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 = 1.57898, size = 290, normalized size = 4.68 \begin{align*} -\frac{2587464000 \, x^{5} + 16430396400 \, x^{4} + 68774793120 \, x^{3} - 82391322420 \, x^{2} - 128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) + 31903287500 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 53550930620 \, x + 28771483125}{106480000 \,{\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 = 0.166316, size = 51, normalized size = 0.82 \begin{align*} - \frac{243 x^{3}}{40} - \frac{35721 x^{2}}{800} - \frac{102303 x}{500} + \frac{10958164 x - 4184943}{61952 x^{2} - 61952 x + 15488} - \frac{12761315 \log{\left (x - \frac{1}{2} \right )}}{42592} + \frac{\log{\left (x + \frac{3}{5} \right )}}{831875} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.91749, size = 62, normalized size = 1. \begin{align*} -\frac{243}{40} \, x^{3} - \frac{35721}{800} \, x^{2} - \frac{102303}{500} \, x + \frac{16807 \,{\left (652 \, x - 249\right )}}{15488 \,{\left (2 \, x - 1\right )}^{2}} + \frac{1}{831875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{12761315}{42592} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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