Optimal. Leaf size=59 \[ \frac {184877}{256 (1-2 x)^2}-\frac {60025}{16 (1-2 x)}-\frac {109089 x}{32}-\frac {16821 x^2}{16}-\frac {4401 x^3}{16}-\frac {1215 x^4}{32}-\frac {519645}{128} \log (1-2 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 59, 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 = {78}
\begin {gather*} -\frac {1215 x^4}{32}-\frac {4401 x^3}{16}-\frac {16821 x^2}{16}-\frac {109089 x}{32}-\frac {60025}{16 (1-2 x)}+\frac {184877}{256 (1-2 x)^2}-\frac {519645}{128} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-\frac {109089}{32}-\frac {16821 x}{8}-\frac {13203 x^2}{16}-\frac {1215 x^3}{8}-\frac {184877}{64 (-1+2 x)^3}-\frac {60025}{8 (-1+2 x)^2}-\frac {519645}{64 (-1+2 x)}\right ) \, dx\\ &=\frac {184877}{256 (1-2 x)^2}-\frac {60025}{16 (1-2 x)}-\frac {109089 x}{32}-\frac {16821 x^2}{16}-\frac {4401 x^3}{16}-\frac {1215 x^4}{32}-\frac {519645}{128} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 56, normalized size = 0.95 \begin {gather*} -\frac {524947+2008220 x-10547820 x^2+4969440 x^3+1609200 x^4+485568 x^5+77760 x^6+2078580 (1-2 x)^2 \log (1-2 x)}{512 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 46, normalized size = 0.78
method | result | size |
risch | \(-\frac {1215 x^{4}}{32}-\frac {4401 x^{3}}{16}-\frac {16821 x^{2}}{16}-\frac {109089 x}{32}+\frac {\frac {60025 x}{8}-\frac {775523}{256}}{\left (-1+2 x \right )^{2}}-\frac {519645 \ln \left (-1+2 x \right )}{128}\) | \(42\) |
default | \(-\frac {1215 x^{4}}{32}-\frac {4401 x^{3}}{16}-\frac {16821 x^{2}}{16}-\frac {109089 x}{32}+\frac {60025}{16 \left (-1+2 x \right )}+\frac {184877}{256 \left (-1+2 x \right )^{2}}-\frac {519645 \ln \left (-1+2 x \right )}{128}\) | \(46\) |
norman | \(\frac {-\frac {513501}{64} x +\frac {1580951}{64} x^{2}-\frac {155295}{16} x^{3}-\frac {100575}{32} x^{4}-\frac {7587}{8} x^{5}-\frac {1215}{8} x^{6}}{\left (-1+2 x \right )^{2}}-\frac {519645 \ln \left (-1+2 x \right )}{128}\) | \(47\) |
meijerg | \(\frac {48 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {440 x^{2}}{\left (1-2 x \right )^{2}}-\frac {140 x \left (-18 x +6\right )}{\left (1-2 x \right )^{2}}-\frac {519645 \ln \left (1-2 x \right )}{128}-\frac {855 x \left (16 x^{2}-36 x +12\right )}{4 \left (1-2 x \right )^{2}}-\frac {783 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{16 \left (1-2 x \right )^{2}}-\frac {1593 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{64 \left (1-2 x \right )^{2}}-\frac {1215 x \left (224 x^{5}+224 x^{4}+280 x^{3}+560 x^{2}-1260 x +420\right )}{1792 \left (1-2 x \right )^{2}}\) | \(162\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.60, size = 46, normalized size = 0.78 \begin {gather*} -\frac {1215}{32} \, x^{4} - \frac {4401}{16} \, x^{3} - \frac {16821}{16} \, x^{2} - \frac {109089}{32} \, x + \frac {2401 \, {\left (800 \, x - 323\right )}}{256 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {519645}{128} \, \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 = 0.39, size = 62, normalized size = 1.05 \begin {gather*} -\frac {38880 \, x^{6} + 242784 \, x^{5} + 804600 \, x^{4} + 2484720 \, x^{3} - 3221712 \, x^{2} + 1039290 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1048088 \, x + 775523}{256 \, {\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 = 0.07, size = 51, normalized size = 0.86 \begin {gather*} - \frac {1215 x^{4}}{32} - \frac {4401 x^{3}}{16} - \frac {16821 x^{2}}{16} - \frac {109089 x}{32} - \frac {775523 - 1920800 x}{1024 x^{2} - 1024 x + 256} - \frac {519645 \log {\left (2 x - 1 \right )}}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.70, size = 42, normalized size = 0.71 \begin {gather*} -\frac {1215}{32} \, x^{4} - \frac {4401}{16} \, x^{3} - \frac {16821}{16} \, x^{2} - \frac {109089}{32} \, x + \frac {2401 \, {\left (800 \, x - 323\right )}}{256 \, {\left (2 \, x - 1\right )}^{2}} - \frac {519645}{128} \, \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 = 41, normalized size = 0.69 \begin {gather*} \frac {\frac {60025\,x}{32}-\frac {775523}{1024}}{x^2-x+\frac {1}{4}}-\frac {519645\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {109089\,x}{32}-\frac {16821\,x^2}{16}-\frac {4401\,x^3}{16}-\frac {1215\,x^4}{32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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