Optimal. Leaf size=65 \[ -\frac {10935 x^8}{16}-\frac {126117 x^7}{28}-\frac {218943 x^6}{16}-\frac {2053917 x^5}{80}-\frac {4352157 x^4}{128}-\frac {2257119 x^3}{64}-\frac {8362653 x^2}{256}-\frac {8960669 x}{256}-\frac {9058973}{512} \log (1-2 x) \]
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Rubi [A] time = 0.02, antiderivative size = 65, 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 = {77} \[ -\frac {10935 x^8}{16}-\frac {126117 x^7}{28}-\frac {218943 x^6}{16}-\frac {2053917 x^5}{80}-\frac {4352157 x^4}{128}-\frac {2257119 x^3}{64}-\frac {8362653 x^2}{256}-\frac {8960669 x}{256}-\frac {9058973}{512} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^7 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac {8960669}{256}-\frac {8362653 x}{128}-\frac {6771357 x^2}{64}-\frac {4352157 x^3}{32}-\frac {2053917 x^4}{16}-\frac {656829 x^5}{8}-\frac {126117 x^6}{4}-\frac {10935 x^7}{2}-\frac {9058973}{256 (-1+2 x)}\right ) \, dx\\ &=-\frac {8960669 x}{256}-\frac {8362653 x^2}{256}-\frac {2257119 x^3}{64}-\frac {4352157 x^4}{128}-\frac {2053917 x^5}{80}-\frac {218943 x^6}{16}-\frac {126117 x^7}{28}-\frac {10935 x^8}{16}-\frac {9058973}{512} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 52, normalized size = 0.80 \[ \frac {-97977600 x^8-645719040 x^7-1961729280 x^6-3680619264 x^5-4874415840 x^4-5055946560 x^3-4683085680 x^2-5017974640 x-2536512440 \log (1-2 x)+4767501827}{143360} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 47, normalized size = 0.72 \[ -\frac {10935}{16} \, x^{8} - \frac {126117}{28} \, x^{7} - \frac {218943}{16} \, x^{6} - \frac {2053917}{80} \, x^{5} - \frac {4352157}{128} \, x^{4} - \frac {2257119}{64} \, x^{3} - \frac {8362653}{256} \, x^{2} - \frac {8960669}{256} \, x - \frac {9058973}{512} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 48, normalized size = 0.74 \[ -\frac {10935}{16} \, x^{8} - \frac {126117}{28} \, x^{7} - \frac {218943}{16} \, x^{6} - \frac {2053917}{80} \, x^{5} - \frac {4352157}{128} \, x^{4} - \frac {2257119}{64} \, x^{3} - \frac {8362653}{256} \, x^{2} - \frac {8960669}{256} \, x - \frac {9058973}{512} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 48, normalized size = 0.74 \[ -\frac {10935 x^{8}}{16}-\frac {126117 x^{7}}{28}-\frac {218943 x^{6}}{16}-\frac {2053917 x^{5}}{80}-\frac {4352157 x^{4}}{128}-\frac {2257119 x^{3}}{64}-\frac {8362653 x^{2}}{256}-\frac {8960669 x}{256}-\frac {9058973 \ln \left (2 x -1\right )}{512} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 47, normalized size = 0.72 \[ -\frac {10935}{16} \, x^{8} - \frac {126117}{28} \, x^{7} - \frac {218943}{16} \, x^{6} - \frac {2053917}{80} \, x^{5} - \frac {4352157}{128} \, x^{4} - \frac {2257119}{64} \, x^{3} - \frac {8362653}{256} \, x^{2} - \frac {8960669}{256} \, x - \frac {9058973}{512} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 45, normalized size = 0.69 \[ -\frac {8960669\,x}{256}-\frac {9058973\,\ln \left (x-\frac {1}{2}\right )}{512}-\frac {8362653\,x^2}{256}-\frac {2257119\,x^3}{64}-\frac {4352157\,x^4}{128}-\frac {2053917\,x^5}{80}-\frac {218943\,x^6}{16}-\frac {126117\,x^7}{28}-\frac {10935\,x^8}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 63, normalized size = 0.97 \[ - \frac {10935 x^{8}}{16} - \frac {126117 x^{7}}{28} - \frac {218943 x^{6}}{16} - \frac {2053917 x^{5}}{80} - \frac {4352157 x^{4}}{128} - \frac {2257119 x^{3}}{64} - \frac {8362653 x^{2}}{256} - \frac {8960669 x}{256} - \frac {9058973 \log {\left (2 x - 1 \right )}}{512} \]
Verification of antiderivative is not currently implemented for this CAS.
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