Optimal. Leaf size=44 \[ -\frac {39199 x}{32}-\frac {30175 x^2}{32}-\frac {5349 x^3}{8}-\frac {4995 x^4}{16}-\frac {135 x^5}{2}-\frac {41503}{64} \log (1-2 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 44, 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 = {90}
\begin {gather*} -\frac {135 x^5}{2}-\frac {4995 x^4}{16}-\frac {5349 x^3}{8}-\frac {30175 x^2}{32}-\frac {39199 x}{32}-\frac {41503}{64} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac {39199}{32}-\frac {30175 x}{16}-\frac {16047 x^2}{8}-\frac {4995 x^3}{4}-\frac {675 x^4}{2}-\frac {41503}{32 (-1+2 x)}\right ) \, dx\\ &=-\frac {39199 x}{32}-\frac {30175 x^2}{32}-\frac {5349 x^3}{8}-\frac {4995 x^4}{16}-\frac {135 x^5}{2}-\frac {41503}{64} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 37, normalized size = 0.84 \begin {gather*} \frac {1}{256} \left (244077-313592 x-241400 x^2-171168 x^3-79920 x^4-17280 x^5-166012 \log (1-2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 33, normalized size = 0.75
method | result | size |
default | \(-\frac {135 x^{5}}{2}-\frac {4995 x^{4}}{16}-\frac {5349 x^{3}}{8}-\frac {30175 x^{2}}{32}-\frac {39199 x}{32}-\frac {41503 \ln \left (-1+2 x \right )}{64}\) | \(33\) |
norman | \(-\frac {135 x^{5}}{2}-\frac {4995 x^{4}}{16}-\frac {5349 x^{3}}{8}-\frac {30175 x^{2}}{32}-\frac {39199 x}{32}-\frac {41503 \ln \left (-1+2 x \right )}{64}\) | \(33\) |
risch | \(-\frac {135 x^{5}}{2}-\frac {4995 x^{4}}{16}-\frac {5349 x^{3}}{8}-\frac {30175 x^{2}}{32}-\frac {39199 x}{32}-\frac {41503 \ln \left (-1+2 x \right )}{64}\) | \(33\) |
meijerg | \(-\frac {41503 \ln \left (1-2 x \right )}{64}-282 x -\frac {883 x \left (6 x +6\right )}{12}-\frac {921 x \left (16 x^{2}+12 x +12\right )}{32}-\frac {9 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{4}-\frac {45 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{128}\) | \(75\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 32, normalized size = 0.73 \begin {gather*} -\frac {135}{2} \, x^{5} - \frac {4995}{16} \, x^{4} - \frac {5349}{8} \, x^{3} - \frac {30175}{32} \, x^{2} - \frac {39199}{32} \, x - \frac {41503}{64} \, \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 = 0.56, size = 32, normalized size = 0.73 \begin {gather*} -\frac {135}{2} \, x^{5} - \frac {4995}{16} \, x^{4} - \frac {5349}{8} \, x^{3} - \frac {30175}{32} \, x^{2} - \frac {39199}{32} \, x - \frac {41503}{64} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 42, normalized size = 0.95 \begin {gather*} - \frac {135 x^{5}}{2} - \frac {4995 x^{4}}{16} - \frac {5349 x^{3}}{8} - \frac {30175 x^{2}}{32} - \frac {39199 x}{32} - \frac {41503 \log {\left (2 x - 1 \right )}}{64} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.85, size = 33, normalized size = 0.75 \begin {gather*} -\frac {135}{2} \, x^{5} - \frac {4995}{16} \, x^{4} - \frac {5349}{8} \, x^{3} - \frac {30175}{32} \, x^{2} - \frac {39199}{32} \, x - \frac {41503}{64} \, \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 = 30, normalized size = 0.68 \begin {gather*} -\frac {39199\,x}{32}-\frac {41503\,\ln \left (x-\frac {1}{2}\right )}{64}-\frac {30175\,x^2}{32}-\frac {5349\,x^3}{8}-\frac {4995\,x^4}{16}-\frac {135\,x^5}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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