Optimal. Leaf size=52 \[ \frac {41503}{128 (1-2 x)^2}-\frac {91091}{64 (1-2 x)}-\frac {14031 x}{16}-\frac {6345 x^2}{32}-\frac {225 x^3}{8}-\frac {39977}{32} \log (1-2 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 52, 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 {225 x^3}{8}-\frac {6345 x^2}{32}-\frac {14031 x}{16}-\frac {91091}{64 (1-2 x)}+\frac {41503}{128 (1-2 x)^2}-\frac {39977}{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)^3 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac {14031}{16}-\frac {6345 x}{16}-\frac {675 x^2}{8}-\frac {41503}{32 (-1+2 x)^3}-\frac {91091}{32 (-1+2 x)^2}-\frac {39977}{16 (-1+2 x)}\right ) \, dx\\ &=\frac {41503}{128 (1-2 x)^2}-\frac {91091}{64 (1-2 x)}-\frac {14031 x}{16}-\frac {6345 x^2}{32}-\frac {225 x^3}{8}-\frac {39977}{32} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 47, normalized size = 0.90 \begin {gather*} \frac {1}{32} \left (-\frac {2 \left (9720-55 x-84411 x^2+43884 x^3+10890 x^4+1800 x^5\right )}{(1-2 x)^2}-39977 \log (1-2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 41, normalized size = 0.79
method | result | size |
risch | \(-\frac {225 x^{3}}{8}-\frac {6345 x^{2}}{32}-\frac {14031 x}{16}+\frac {\frac {91091 x}{32}-\frac {140679}{128}}{\left (-1+2 x \right )^{2}}-\frac {39977 \ln \left (-1+2 x \right )}{32}\) | \(37\) |
default | \(-\frac {225 x^{3}}{8}-\frac {6345 x^{2}}{32}-\frac {14031 x}{16}+\frac {91091}{64 \left (-1+2 x \right )}+\frac {41503}{128 \left (-1+2 x \right )^{2}}-\frac {39977 \ln \left (-1+2 x \right )}{32}\) | \(41\) |
norman | \(\frac {-\frac {38825}{16} x +\frac {123291}{16} x^{2}-\frac {10971}{4} x^{3}-\frac {5445}{8} x^{4}-\frac {225}{2} x^{5}}{\left (-1+2 x \right )^{2}}-\frac {39977 \ln \left (-1+2 x \right )}{32}\) | \(42\) |
meijerg | \(\frac {36 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {282 x^{2}}{\left (1-2 x \right )^{2}}-\frac {883 x \left (-18 x +6\right )}{12 \left (1-2 x \right )^{2}}-\frac {39977 \ln \left (1-2 x \right )}{32}-\frac {2763 x \left (16 x^{2}-36 x +12\right )}{32 \left (1-2 x \right )^{2}}-\frac {27 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{2 \left (1-2 x \right )^{2}}-\frac {225 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{64 \left (1-2 x \right )^{2}}\) | \(127\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 41, normalized size = 0.79 \begin {gather*} -\frac {225}{8} \, x^{3} - \frac {6345}{32} \, x^{2} - \frac {14031}{16} \, x + \frac {539 \, {\left (676 \, x - 261\right )}}{128 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {39977}{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 = 0.47, size = 57, normalized size = 1.10 \begin {gather*} -\frac {14400 \, x^{5} + 87120 \, x^{4} + 351072 \, x^{3} - 423612 \, x^{2} + 159908 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 252116 \, x + 140679}{128 \, {\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 = 0.06, size = 44, normalized size = 0.85 \begin {gather*} - \frac {225 x^{3}}{8} - \frac {6345 x^{2}}{32} - \frac {14031 x}{16} - \frac {140679 - 364364 x}{512 x^{2} - 512 x + 128} - \frac {39977 \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 = 0.56, size = 37, normalized size = 0.71 \begin {gather*} -\frac {225}{8} \, x^{3} - \frac {6345}{32} \, x^{2} - \frac {14031}{16} \, x + \frac {539 \, {\left (676 \, x - 261\right )}}{128 \, {\left (2 \, x - 1\right )}^{2}} - \frac {39977}{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 = 0.03, size = 36, normalized size = 0.69 \begin {gather*} \frac {\frac {91091\,x}{128}-\frac {140679}{512}}{x^2-x+\frac {1}{4}}-\frac {39977\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {14031\,x}{16}-\frac {6345\,x^2}{32}-\frac {225\,x^3}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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