Optimal. Leaf size=80 \[ \frac {156590819}{2048 (1-2 x)^2}-\frac {616195041}{1024 (1-2 x)}-\frac {308539921 x}{256}-\frac {306103815 x^2}{512}-\frac {41793093 x^3}{128}-\frac {19986237 x^4}{128}-\frac {229149 x^5}{4}-\frac {443475 x^6}{32}-\frac {91125 x^7}{56}-\frac {33674025}{32} \log (1-2 x) \]
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Rubi [A]
time = 0.03, 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 = {90}
\begin {gather*} -\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) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
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 = 0.02, size = 71, normalized size = 0.89 \begin {gather*} -\frac {-1001301969+11541996324 x-26671311588 x^2+9877535360 x^3+4449695040 x^4+2647685376 x^5+1466857728 x^6+628425216 x^7+175348800 x^8+23328000 x^9+3771490800 (1-2 x)^2 \log (1-2 x)}{3584 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 61, normalized size = 0.76
method | result | size |
risch | \(-\frac {91125 x^{7}}{56}-\frac {443475 x^{6}}{32}-\frac {229149 x^{5}}{4}-\frac {19986237 x^{4}}{128}-\frac {41793093 x^{3}}{128}-\frac {306103815 x^{2}}{512}-\frac {308539921 x}{256}+\frac {\frac {616195041 x}{512}-\frac {1075799263}{2048}}{\left (-1+2 x \right )^{2}}-\frac {33674025 \ln \left (-1+2 x \right )}{32}\) | \(57\) |
default | \(-\frac {91125 x^{7}}{56}-\frac {443475 x^{6}}{32}-\frac {229149 x^{5}}{4}-\frac {19986237 x^{4}}{128}-\frac {41793093 x^{3}}{128}-\frac {306103815 x^{2}}{512}-\frac {308539921 x}{256}+\frac {616195041}{1024 \left (-1+2 x \right )}+\frac {156590819}{2048 \left (-1+2 x \right )^{2}}-\frac {33674025 \ln \left (-1+2 x \right )}{32}\) | \(61\) |
norman | \(\frac {-\frac {33646377}{16} x +\frac {101187963}{16} x^{2}-\frac {11024035}{4} x^{3}-\frac {9932355}{8} x^{4}-\frac {1477503}{2} x^{5}-\frac {818559}{2} x^{6}-\frac {1227393}{7} x^{7}-\frac {2739825}{56} x^{8}-\frac {91125}{14} x^{9}}{\left (-1+2 x \right )^{2}}-\frac {33674025 \ln \left (-1+2 x \right )}{32}\) | \(62\) |
meijerg | \(\frac {864 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}-\frac {11745 x \left (1920 x^{7}+1536 x^{6}+1344 x^{5}+1344 x^{4}+1680 x^{3}+3360 x^{2}-7560 x +2520\right )}{512 \left (1-2 x \right )^{2}}-\frac {33674025 \ln \left (1-2 x \right )}{32}-\frac {18225 x \left (2560 x^{8}+1920 x^{7}+1536 x^{6}+1344 x^{5}+1344 x^{4}+1680 x^{3}+3360 x^{2}-7560 x +2520\right )}{7168 \left (1-2 x \right )^{2}}-\frac {272403 x \left (512 x^{6}+448 x^{5}+448 x^{4}+560 x^{3}+1120 x^{2}-2520 x +840\right )}{1024 \left (1-2 x \right )^{2}}-\frac {2046843 x \left (224 x^{5}+224 x^{4}+280 x^{3}+560 x^{2}-1260 x +420\right )}{1792 \left (1-2 x \right )^{2}}-\frac {10296 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{\left (1-2 x \right )^{2}}-\frac {63621 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{8 \left (1-2 x \right )^{2}}-\frac {34115 x \left (16 x^{2}-36 x +12\right )}{2 \left (1-2 x \right )^{2}}-\frac {6270 x \left (-18 x +6\right )}{\left (1-2 x \right )^{2}}+\frac {12096 x^{2}}{\left (1-2 x \right )^{2}}\) | \(297\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.41, size = 61, normalized size = 0.76 \begin {gather*} -\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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 77, normalized size = 0.96 \begin {gather*} -\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 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 71, normalized size = 0.89 \begin {gather*} - \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.59, size = 57, normalized size = 0.71 \begin {gather*} -\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 ) \end {gather*}
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 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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