Optimal. Leaf size=32 \[ \frac {539}{16 (1-2 x)}+33 x+\frac {45 x^2}{8}+\frac {707}{16} \log (1-2 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 32, 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 {45 x^2}{8}+33 x+\frac {539}{16 (1-2 x)}+\frac {707}{16} \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)^2 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (33+\frac {45 x}{4}+\frac {539}{8 (-1+2 x)^2}+\frac {707}{8 (-1+2 x)}\right ) \, dx\\ &=\frac {539}{16 (1-2 x)}+33 x+\frac {45 x^2}{8}+\frac {707}{16} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 36, normalized size = 1.12 \begin {gather*} \frac {-505-2202 x+1932 x^2+360 x^3+1414 (-1+2 x) \log (1-2 x)}{-32+64 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 27, normalized size = 0.84
method | result | size |
risch | \(\frac {45 x^{2}}{8}+33 x -\frac {539}{32 \left (-\frac {1}{2}+x \right )}+\frac {707 \ln \left (-1+2 x \right )}{16}\) | \(25\) |
default | \(\frac {45 x^{2}}{8}+33 x -\frac {539}{16 \left (-1+2 x \right )}+\frac {707 \ln \left (-1+2 x \right )}{16}\) | \(27\) |
norman | \(\frac {-\frac {803}{8} x +\frac {483}{8} x^{2}+\frac {45}{4} x^{3}}{-1+2 x}+\frac {707 \ln \left (-1+2 x \right )}{16}\) | \(32\) |
meijerg | \(\frac {40 x}{1-2 x}+\frac {707 \ln \left (1-2 x \right )}{16}+\frac {29 x \left (-6 x +6\right )}{4 \left (1-2 x \right )}+\frac {45 x \left (-8 x^{2}-12 x +12\right )}{32 \left (1-2 x \right )}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 26, normalized size = 0.81 \begin {gather*} \frac {45}{8} \, x^{2} + 33 \, x - \frac {539}{16 \, {\left (2 \, x - 1\right )}} + \frac {707}{16} \, \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 = 1.24, size = 37, normalized size = 1.16 \begin {gather*} \frac {180 \, x^{3} + 966 \, x^{2} + 707 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 528 \, x - 539}{16 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 26, normalized size = 0.81 \begin {gather*} \frac {45 x^{2}}{8} + 33 x + \frac {707 \log {\left (2 x - 1 \right )}}{16} - \frac {539}{32 x - 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.41, size = 48, normalized size = 1.50 \begin {gather*} \frac {3}{32} \, {\left (2 \, x - 1\right )}^{2} {\left (\frac {206}{2 \, x - 1} + 15\right )} - \frac {539}{16 \, {\left (2 \, x - 1\right )}} - \frac {707}{16} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 24, normalized size = 0.75 \begin {gather*} 33\,x+\frac {707\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {539}{32\,\left (x-\frac {1}{2}\right )}+\frac {45\,x^2}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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