Optimal. Leaf size=58 \[ -\frac {1996783 x}{128}-\frac {1797103 x^2}{128}-\frac {444581 x^3}{32}-\frac {736623 x^4}{64}-\frac {275103 x^5}{40}-\frac {20385 x^6}{8}-\frac {6075 x^7}{14}-\frac {2033647}{256} \log (1-2 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 58, 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 {6075 x^7}{14}-\frac {20385 x^6}{8}-\frac {275103 x^5}{40}-\frac {736623 x^4}{64}-\frac {444581 x^3}{32}-\frac {1797103 x^2}{128}-\frac {1996783 x}{128}-\frac {2033647}{256} \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)^5 (3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac {1996783}{128}-\frac {1797103 x}{64}-\frac {1333743 x^2}{32}-\frac {736623 x^3}{16}-\frac {275103 x^4}{8}-\frac {61155 x^5}{4}-\frac {6075 x^6}{2}-\frac {2033647}{128 (-1+2 x)}\right ) \, dx\\ &=-\frac {1996783 x}{128}-\frac {1797103 x^2}{128}-\frac {444581 x^3}{32}-\frac {736623 x^4}{64}-\frac {275103 x^5}{40}-\frac {20385 x^6}{8}-\frac {6075 x^7}{14}-\frac {2033647}{256} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 47, normalized size = 0.81 \begin {gather*} \frac {502621309-559099240 x-503188840 x^2-497930720 x^3-412508880 x^4-246492288 x^5-91324800 x^6-15552000 x^7-284710580 \log (1-2 x)}{35840} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 43, normalized size = 0.74
method | result | size |
default | \(-\frac {6075 x^{7}}{14}-\frac {20385 x^{6}}{8}-\frac {275103 x^{5}}{40}-\frac {736623 x^{4}}{64}-\frac {444581 x^{3}}{32}-\frac {1797103 x^{2}}{128}-\frac {1996783 x}{128}-\frac {2033647 \ln \left (-1+2 x \right )}{256}\) | \(43\) |
norman | \(-\frac {6075 x^{7}}{14}-\frac {20385 x^{6}}{8}-\frac {275103 x^{5}}{40}-\frac {736623 x^{4}}{64}-\frac {444581 x^{3}}{32}-\frac {1797103 x^{2}}{128}-\frac {1996783 x}{128}-\frac {2033647 \ln \left (-1+2 x \right )}{256}\) | \(43\) |
risch | \(-\frac {6075 x^{7}}{14}-\frac {20385 x^{6}}{8}-\frac {275103 x^{5}}{40}-\frac {736623 x^{4}}{64}-\frac {444581 x^{3}}{32}-\frac {1797103 x^{2}}{128}-\frac {1996783 x}{128}-\frac {2033647 \ln \left (-1+2 x \right )}{256}\) | \(43\) |
meijerg | \(-\frac {2033647 \ln \left (1-2 x \right )}{256}-1560 x -\frac {1810 x \left (6 x +6\right )}{3}-\frac {1555 x \left (16 x^{2}+12 x +12\right )}{4}-\frac {1923 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{32}-\frac {17829 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{640}-\frac {459 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{448}-\frac {405 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{7168}\) | \(136\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.39, size = 42, normalized size = 0.72 \begin {gather*} -\frac {6075}{14} \, x^{7} - \frac {20385}{8} \, x^{6} - \frac {275103}{40} \, x^{5} - \frac {736623}{64} \, x^{4} - \frac {444581}{32} \, x^{3} - \frac {1797103}{128} \, x^{2} - \frac {1996783}{128} \, x - \frac {2033647}{256} \, \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 = 0.75, size = 42, normalized size = 0.72 \begin {gather*} -\frac {6075}{14} \, x^{7} - \frac {20385}{8} \, x^{6} - \frac {275103}{40} \, x^{5} - \frac {736623}{64} \, x^{4} - \frac {444581}{32} \, x^{3} - \frac {1797103}{128} \, x^{2} - \frac {1996783}{128} \, x - \frac {2033647}{256} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 56, normalized size = 0.97 \begin {gather*} - \frac {6075 x^{7}}{14} - \frac {20385 x^{6}}{8} - \frac {275103 x^{5}}{40} - \frac {736623 x^{4}}{64} - \frac {444581 x^{3}}{32} - \frac {1797103 x^{2}}{128} - \frac {1996783 x}{128} - \frac {2033647 \log {\left (2 x - 1 \right )}}{256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.34, size = 43, normalized size = 0.74 \begin {gather*} -\frac {6075}{14} \, x^{7} - \frac {20385}{8} \, x^{6} - \frac {275103}{40} \, x^{5} - \frac {736623}{64} \, x^{4} - \frac {444581}{32} \, x^{3} - \frac {1797103}{128} \, x^{2} - \frac {1996783}{128} \, x - \frac {2033647}{256} \, \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 = 40, normalized size = 0.69 \begin {gather*} -\frac {1996783\,x}{128}-\frac {2033647\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {1797103\,x^2}{128}-\frac {444581\,x^3}{32}-\frac {736623\,x^4}{64}-\frac {275103\,x^5}{40}-\frac {20385\,x^6}{8}-\frac {6075\,x^7}{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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