Optimal. Leaf size=64 \[ \frac {3195731}{512 (1-2 x)^2}-\frac {9836211}{256 (1-2 x)}-\frac {6277415 x}{128}-\frac {1208973 x^2}{64}-7065 x^3-\frac {120825 x^4}{64}-\frac {2025 x^5}{8}-\frac {12973191}{256} \log (1-2 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 64, 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 {2025 x^5}{8}-\frac {120825 x^4}{64}-7065 x^3-\frac {1208973 x^2}{64}-\frac {6277415 x}{128}-\frac {9836211}{256 (1-2 x)}+\frac {3195731}{512 (1-2 x)^2}-\frac {12973191}{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)^4 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac {6277415}{128}-\frac {1208973 x}{32}-21195 x^2-\frac {120825 x^3}{16}-\frac {10125 x^4}{8}-\frac {3195731}{128 (-1+2 x)^3}-\frac {9836211}{128 (-1+2 x)^2}-\frac {12973191}{128 (-1+2 x)}\right ) \, dx\\ &=\frac {3195731}{512 (1-2 x)^2}-\frac {9836211}{256 (1-2 x)}-\frac {6277415 x}{128}-\frac {1208973 x^2}{64}-7065 x^3-\frac {120825 x^4}{64}-\frac {2025 x^5}{8}-\frac {12973191}{256} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 61, normalized size = 0.95 \begin {gather*} -\frac {1974585+95444820 x-305448900 x^2+130737568 x^3+50369232 x^4+21464640 x^5+6696000 x^6+1036800 x^7+51892764 (1-2 x)^2 \log (1-2 x)}{1024 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 51, normalized size = 0.80
method | result | size |
risch | \(-\frac {2025 x^{5}}{8}-\frac {120825 x^{4}}{64}-7065 x^{3}-\frac {1208973 x^{2}}{64}-\frac {6277415 x}{128}+\frac {\frac {9836211 x}{128}-\frac {16476691}{512}}{\left (-1+2 x \right )^{2}}-\frac {12973191 \ln \left (-1+2 x \right )}{256}\) | \(47\) |
default | \(-\frac {2025 x^{5}}{8}-\frac {120825 x^{4}}{64}-7065 x^{3}-\frac {1208973 x^{2}}{64}-\frac {6277415 x}{128}+\frac {9836211}{256 \left (-1+2 x \right )}+\frac {3195731}{512 \left (-1+2 x \right )^{2}}-\frac {12973191 \ln \left (-1+2 x \right )}{256}\) | \(51\) |
norman | \(\frac {-\frac {12917895}{128} x +\frac {39168405}{128} x^{2}-\frac {4085549}{32} x^{3}-\frac {3148077}{64} x^{4}-\frac {335385}{16} x^{5}-\frac {104625}{16} x^{6}-\frac {2025}{2} x^{7}}{\left (-1+2 x \right )^{2}}-\frac {12973191 \ln \left (-1+2 x \right )}{256}\) | \(52\) |
meijerg | \(\frac {216 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {2376 x^{2}}{\left (1-2 x \right )^{2}}-\frac {933 x \left (-18 x +6\right )}{\left (1-2 x \right )^{2}}-\frac {12973191 \ln \left (1-2 x \right )}{256}-\frac {1831 x \left (16 x^{2}-36 x +12\right )}{\left (1-2 x \right )^{2}}-\frac {91947 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{160 \left (1-2 x \right )^{2}}-\frac {28845 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{64 \left (1-2 x \right )^{2}}-\frac {45225 x \left (224 x^{5}+224 x^{4}+280 x^{3}+560 x^{2}-1260 x +420\right )}{1792 \left (1-2 x \right )^{2}}-\frac {2025 x \left (512 x^{6}+448 x^{5}+448 x^{4}+560 x^{3}+1120 x^{2}-2520 x +840\right )}{1024 \left (1-2 x \right )^{2}}\) | \(202\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 51, normalized size = 0.80 \begin {gather*} -\frac {2025}{8} \, x^{5} - \frac {120825}{64} \, x^{4} - 7065 \, x^{3} - \frac {1208973}{64} \, x^{2} - \frac {6277415}{128} \, x + \frac {41503 \, {\left (948 \, x - 397\right )}}{512 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {12973191}{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 = 0.36, size = 67, normalized size = 1.05 \begin {gather*} -\frac {518400 \, x^{7} + 3348000 \, x^{6} + 10732320 \, x^{5} + 25184616 \, x^{4} + 65368784 \, x^{3} - 90766856 \, x^{2} + 25946382 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 14235184 \, x + 16476691}{512 \, {\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 = 56, normalized size = 0.88 \begin {gather*} - \frac {2025 x^{5}}{8} - \frac {120825 x^{4}}{64} - 7065 x^{3} - \frac {1208973 x^{2}}{64} - \frac {6277415 x}{128} - \frac {16476691 - 39344844 x}{2048 x^{2} - 2048 x + 512} - \frac {12973191 \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 = 1.18, size = 47, normalized size = 0.73 \begin {gather*} -\frac {2025}{8} \, x^{5} - \frac {120825}{64} \, x^{4} - 7065 \, x^{3} - \frac {1208973}{64} \, x^{2} - \frac {6277415}{128} \, x + \frac {41503 \, {\left (948 \, x - 397\right )}}{512 \, {\left (2 \, x - 1\right )}^{2}} - \frac {12973191}{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 = 46, normalized size = 0.72 \begin {gather*} \frac {\frac {9836211\,x}{512}-\frac {16476691}{2048}}{x^2-x+\frac {1}{4}}-\frac {12973191\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {6277415\,x}{128}-\frac {1208973\,x^2}{64}-7065\,x^3-\frac {120825\,x^4}{64}-\frac {2025\,x^5}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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