Optimal. Leaf size=80 \[ -\frac {32805 x^7}{56}-\frac {162567 x^6}{32}-\frac {213597 x^5}{10}-\frac {7568235 x^4}{128}-\frac {16042509 x^3}{128}-\frac {118841283 x^2}{512}-\frac {120864213 x}{256}-\frac {246239357}{1024 (1-2 x)}+\frac {63412811}{2048 (1-2 x)^2}-\frac {106237047}{256} \log (1-2 x) \]
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Rubi [A] time = 0.05, antiderivative size = 80, 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} \[ -\frac {32805 x^7}{56}-\frac {162567 x^6}{32}-\frac {213597 x^5}{10}-\frac {7568235 x^4}{128}-\frac {16042509 x^3}{128}-\frac {118841283 x^2}{512}-\frac {120864213 x}{256}-\frac {246239357}{1024 (1-2 x)}+\frac {63412811}{2048 (1-2 x)^2}-\frac {106237047}{256} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^8 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-\frac {120864213}{256}-\frac {118841283 x}{256}-\frac {48127527 x^2}{128}-\frac {7568235 x^3}{32}-\frac {213597 x^4}{2}-\frac {487701 x^5}{16}-\frac {32805 x^6}{8}-\frac {63412811}{512 (-1+2 x)^3}-\frac {246239357}{512 (-1+2 x)^2}-\frac {106237047}{128 (-1+2 x)}\right ) \, dx\\ &=\frac {63412811}{2048 (1-2 x)^2}-\frac {246239357}{1024 (1-2 x)}-\frac {120864213 x}{256}-\frac {118841283 x^2}{512}-\frac {16042509 x^3}{128}-\frac {7568235 x^4}{128}-\frac {213597 x^5}{10}-\frac {162567 x^6}{32}-\frac {32805 x^7}{56}-\frac {106237047}{256} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 71, normalized size = 0.89 \[ -\frac {83980800 x^9+644319360 x^8+2354821632 x^7+5596371648 x^6+10256718528 x^5+17427054960 x^4+38900302560 x^3-104409393876 x^2+44728559236 x+14873186580 (1-2 x)^2 \log (1-2 x)-3752427799}{35840 (1-2 x)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 77, normalized size = 0.96 \[ -\frac {167961600 \, x^{9} + 1288638720 \, x^{8} + 4709643264 \, x^{7} + 11192743296 \, x^{6} + 20513437056 \, x^{5} + 34854109920 \, x^{4} + 77800605120 \, x^{3} - 118730138940 \, x^{2} + 29746373160 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 631530340 \, x + 15017306605}{71680 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.27, size = 57, normalized size = 0.71 \[ -\frac {32805}{56} \, x^{7} - \frac {162567}{32} \, x^{6} - \frac {213597}{10} \, x^{5} - \frac {7568235}{128} \, x^{4} - \frac {16042509}{128} \, x^{3} - \frac {118841283}{512} \, x^{2} - \frac {120864213}{256} \, x + \frac {823543 \, {\left (1196 \, x - 521\right )}}{2048 \, {\left (2 \, x - 1\right )}^{2}} - \frac {106237047}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 61, normalized size = 0.76 \[ -\frac {32805 x^{7}}{56}-\frac {162567 x^{6}}{32}-\frac {213597 x^{5}}{10}-\frac {7568235 x^{4}}{128}-\frac {16042509 x^{3}}{128}-\frac {118841283 x^{2}}{512}-\frac {120864213 x}{256}-\frac {106237047 \ln \left (2 x -1\right )}{256}+\frac {63412811}{2048 \left (2 x -1\right )^{2}}+\frac {246239357}{1024 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 61, normalized size = 0.76 \[ -\frac {32805}{56} \, x^{7} - \frac {162567}{32} \, x^{6} - \frac {213597}{10} \, x^{5} - \frac {7568235}{128} \, x^{4} - \frac {16042509}{128} \, x^{3} - \frac {118841283}{512} \, x^{2} - \frac {120864213}{256} \, x + \frac {823543 \, {\left (1196 \, x - 521\right )}}{2048 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {106237047}{256} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 56, normalized size = 0.70 \[ \frac {\frac {246239357\,x}{2048}-\frac {429065903}{8192}}{x^2-x+\frac {1}{4}}-\frac {106237047\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {120864213\,x}{256}-\frac {118841283\,x^2}{512}-\frac {16042509\,x^3}{128}-\frac {7568235\,x^4}{128}-\frac {213597\,x^5}{10}-\frac {162567\,x^6}{32}-\frac {32805\,x^7}{56} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 71, normalized size = 0.89 \[ - \frac {32805 x^{7}}{56} - \frac {162567 x^{6}}{32} - \frac {213597 x^{5}}{10} - \frac {7568235 x^{4}}{128} - \frac {16042509 x^{3}}{128} - \frac {118841283 x^{2}}{512} - \frac {120864213 x}{256} - \frac {429065903 - 984957428 x}{8192 x^{2} - 8192 x + 2048} - \frac {106237047 \log {\left (2 x - 1 \right )}}{256} \]
Verification of antiderivative is not currently implemented for this CAS.
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