Optimal. Leaf size=45 \[ \frac {9317}{64 (1-2 x)^2}-\frac {8349}{16 (1-2 x)}-\frac {2975 x}{16}-\frac {375 x^2}{16}-\frac {2805}{8} \log (1-2 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} -\frac {375 x^2}{16}-\frac {2975 x}{16}-\frac {8349}{16 (1-2 x)}+\frac {9317}{64 (1-2 x)^2}-\frac {2805}{8} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(2+3 x) (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac {2975}{16}-\frac {375 x}{8}-\frac {9317}{16 (-1+2 x)^3}-\frac {8349}{8 (-1+2 x)^2}-\frac {2805}{4 (-1+2 x)}\right ) \, dx\\ &=\frac {9317}{64 (1-2 x)^2}-\frac {8349}{16 (1-2 x)}-\frac {2975 x}{16}-\frac {375 x^2}{16}-\frac {2805}{8} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 46, normalized size = 1.02 \begin {gather*} -\frac {8877-14796 x-35700 x^2+20800 x^3+3000 x^4+11220 (1-2 x)^2 \log (1-2 x)}{32 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 36, normalized size = 0.80
method | result | size |
risch | \(-\frac {375 x^{2}}{16}-\frac {2975 x}{16}+\frac {\frac {8349 x}{8}-\frac {24079}{64}}{\left (-1+2 x \right )^{2}}-\frac {2805 \ln \left (-1+2 x \right )}{8}\) | \(32\) |
default | \(-\frac {375 x^{2}}{16}-\frac {2975 x}{16}+\frac {8349}{16 \left (-1+2 x \right )}+\frac {9317}{64 \left (-1+2 x \right )^{2}}-\frac {2805 \ln \left (-1+2 x \right )}{8}\) | \(36\) |
norman | \(\frac {-\frac {2589}{4} x +\frac {8901}{4} x^{2}-650 x^{3}-\frac {375}{4} x^{4}}{\left (-1+2 x \right )^{2}}-\frac {2805 \ln \left (-1+2 x \right )}{8}\) | \(37\) |
meijerg | \(\frac {27 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {351 x^{2}}{2 \left (1-2 x \right )^{2}}-\frac {285 x \left (-18 x +6\right )}{8 \left (1-2 x \right )^{2}}-\frac {2805 \ln \left (1-2 x \right )}{8}-\frac {925 x \left (16 x^{2}-36 x +12\right )}{32 \left (1-2 x \right )^{2}}-\frac {75 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{32 \left (1-2 x \right )^{2}}\) | \(97\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 36, normalized size = 0.80 \begin {gather*} -\frac {375}{16} \, x^{2} - \frac {2975}{16} \, x + \frac {121 \, {\left (552 \, x - 199\right )}}{64 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {2805}{8} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.45, size = 52, normalized size = 1.16 \begin {gather*} -\frac {6000 \, x^{4} + 41600 \, x^{3} - 46100 \, x^{2} + 22440 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 54892 \, x + 24079}{64 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 37, normalized size = 0.82 \begin {gather*} - \frac {375 x^{2}}{16} - \frac {2975 x}{16} - \frac {24079 - 66792 x}{256 x^{2} - 256 x + 64} - \frac {2805 \log {\left (2 x - 1 \right )}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.09, size = 32, normalized size = 0.71 \begin {gather*} -\frac {375}{16} \, x^{2} - \frac {2975}{16} \, x + \frac {121 \, {\left (552 \, x - 199\right )}}{64 \, {\left (2 \, x - 1\right )}^{2}} - \frac {2805}{8} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 31, normalized size = 0.69 \begin {gather*} \frac {\frac {8349\,x}{32}-\frac {24079}{256}}{x^2-x+\frac {1}{4}}-\frac {2805\,\ln \left (x-\frac {1}{2}\right )}{8}-\frac {2975\,x}{16}-\frac {375\,x^2}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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