Optimal. Leaf size=80 \[ -\frac {91125 x^7}{56}-\frac {443475 x^6}{32}-\frac {229149 x^5}{4}-\frac {19986237 x^4}{128}-\frac {41793093 x^3}{128}-\frac {306103815 x^2}{512}-\frac {308539921 x}{256}-\frac {616195041}{1024 (1-2 x)}+\frac {156590819}{2048 (1-2 x)^2}-\frac {33674025}{32} \log (1-2 x) \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ -\frac {91125 x^7}{56}-\frac {443475 x^6}{32}-\frac {229149 x^5}{4}-\frac {19986237 x^4}{128}-\frac {41793093 x^3}{128}-\frac {306103815 x^2}{512}-\frac {308539921 x}{256}-\frac {616195041}{1024 (1-2 x)}+\frac {156590819}{2048 (1-2 x)^2}-\frac {33674025}{32} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac {308539921}{256}-\frac {306103815 x}{256}-\frac {125379279 x^2}{128}-\frac {19986237 x^3}{32}-\frac {1145745 x^4}{4}-\frac {1330425 x^5}{16}-\frac {91125 x^6}{8}-\frac {156590819}{512 (-1+2 x)^3}-\frac {616195041}{512 (-1+2 x)^2}-\frac {33674025}{16 (-1+2 x)}\right ) \, dx\\ &=\frac {156590819}{2048 (1-2 x)^2}-\frac {616195041}{1024 (1-2 x)}-\frac {308539921 x}{256}-\frac {306103815 x^2}{512}-\frac {41793093 x^3}{128}-\frac {19986237 x^4}{128}-\frac {229149 x^5}{4}-\frac {443475 x^6}{32}-\frac {91125 x^7}{56}-\frac {33674025}{32} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 71, normalized size = 0.89 \[ -\frac {23328000 x^9+175348800 x^8+628425216 x^7+1466857728 x^6+2647685376 x^5+4449695040 x^4+9877535360 x^3-26671311588 x^2+11541996324 x+3771490800 (1-2 x)^2 \log (1-2 x)-1001301969}{3584 (1-2 x)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 77, normalized size = 0.96 \[ -\frac {93312000 \, x^{9} + 701395200 \, x^{8} + 2513700864 \, x^{7} + 5867430912 \, x^{6} + 10590741504 \, x^{5} + 17798780160 \, x^{4} + 39510141440 \, x^{3} - 60542035484 \, x^{2} + 15085963200 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 24774428 \, x + 7530594841}{14336 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.09, size = 57, normalized size = 0.71 \[ -\frac {91125}{56} \, x^{7} - \frac {443475}{32} \, x^{6} - \frac {229149}{4} \, x^{5} - \frac {19986237}{128} \, x^{4} - \frac {41793093}{128} \, x^{3} - \frac {306103815}{512} \, x^{2} - \frac {308539921}{256} \, x + \frac {2033647 \, {\left (1212 \, x - 529\right )}}{2048 \, {\left (2 \, x - 1\right )}^{2}} - \frac {33674025}{32} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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 \[ -\frac {91125 x^{7}}{56}-\frac {443475 x^{6}}{32}-\frac {229149 x^{5}}{4}-\frac {19986237 x^{4}}{128}-\frac {41793093 x^{3}}{128}-\frac {306103815 x^{2}}{512}-\frac {308539921 x}{256}-\frac {33674025 \ln \left (2 x -1\right )}{32}+\frac {156590819}{2048 \left (2 x -1\right )^{2}}+\frac {616195041}{1024 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 61, normalized size = 0.76 \[ -\frac {91125}{56} \, x^{7} - \frac {443475}{32} \, x^{6} - \frac {229149}{4} \, x^{5} - \frac {19986237}{128} \, x^{4} - \frac {41793093}{128} \, x^{3} - \frac {306103815}{512} \, x^{2} - \frac {308539921}{256} \, x + \frac {2033647 \, {\left (1212 \, x - 529\right )}}{2048 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {33674025}{32} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.06, size = 56, normalized size = 0.70 \[ \frac {\frac {616195041\,x}{2048}-\frac {1075799263}{8192}}{x^2-x+\frac {1}{4}}-\frac {33674025\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {308539921\,x}{256}-\frac {306103815\,x^2}{512}-\frac {41793093\,x^3}{128}-\frac {19986237\,x^4}{128}-\frac {229149\,x^5}{4}-\frac {443475\,x^6}{32}-\frac {91125\,x^7}{56} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 71, normalized size = 0.89 \[ - \frac {91125 x^{7}}{56} - \frac {443475 x^{6}}{32} - \frac {229149 x^{5}}{4} - \frac {19986237 x^{4}}{128} - \frac {41793093 x^{3}}{128} - \frac {306103815 x^{2}}{512} - \frac {308539921 x}{256} - \frac {1075799263 - 2464780164 x}{8192 x^{2} - 8192 x + 2048} - \frac {33674025 \log {\left (2 x - 1 \right )}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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