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 = 0.03, antiderivative size = 62, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.04, 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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fricas [A] time = 0.79, size = 75, normalized size = 1.21 \[ -\frac {2587464000 \, x^{5} + 16430396400 \, x^{4} + 68774793120 \, x^{3} - 82391322420 \, x^{2} - 128 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) + 31903287500 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 53550930620 \, x + 28771483125}{106480000 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 46, normalized size = 0.74 \[ -\frac {243}{40} \, x^{3} - \frac {35721}{800} \, x^{2} - \frac {102303}{500} \, x + \frac {16807 \, {\left (652 \, x - 249\right )}}{15488 \, {\left (2 \, x - 1\right )}^{2}} + \frac {1}{831875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {12761315}{42592} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 49, normalized size = 0.79 \[ -\frac {243 x^{3}}{40}-\frac {35721 x^{2}}{800}-\frac {102303 x}{500}-\frac {12761315 \ln \left (2 x -1\right )}{42592}+\frac {\ln \left (5 x +3\right )}{831875}+\frac {117649}{1408 \left (2 x -1\right )^{2}}+\frac {2739541}{7744 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 49, normalized size = 0.79 \[ -\frac {243}{40} \, x^{3} - \frac {35721}{800} \, x^{2} - \frac {102303}{500} \, x + \frac {16807 \, {\left (652 \, x - 249\right )}}{15488 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {1}{831875} \, \log \left (5 \, x + 3\right ) - \frac {12761315}{42592} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 42, normalized size = 0.68 \[ \frac {\ln \left (x+\frac {3}{5}\right )}{831875}-\frac {12761315\,\ln \left (x-\frac {1}{2}\right )}{42592}-\frac {102303\,x}{500}+\frac {\frac {2739541\,x}{15488}-\frac {4184943}{61952}}{x^2-x+\frac {1}{4}}-\frac {35721\,x^2}{800}-\frac {243\,x^3}{40} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 51, normalized size = 0.82 \[ - \frac {243 x^{3}}{40} - \frac {35721 x^{2}}{800} - \frac {102303 x}{500} - \frac {4184943 - 10958164 x}{61952 x^{2} - 61952 x + 15488} - \frac {12761315 \log {\left (x - \frac {1}{2} \right )}}{42592} + \frac {\log {\left (x + \frac {3}{5} \right )}}{831875} \]
Verification of antiderivative is not currently implemented for this CAS.
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