Optimal. Leaf size=30 \[ -\frac {443 x}{8}-\frac {219 x^2}{8}-\frac {15 x^3}{2}-\frac {539}{16} \log (1-2 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 30, 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 {15 x^3}{2}-\frac {219 x^2}{8}-\frac {443 x}{8}-\frac {539}{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} \, dx &=\int \left (-\frac {443}{8}-\frac {219 x}{4}-\frac {45 x^2}{2}-\frac {539}{8 (-1+2 x)}\right ) \, dx\\ &=-\frac {443 x}{8}-\frac {219 x^2}{8}-\frac {15 x^3}{2}-\frac {539}{16} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 0.90 \begin {gather*} \frac {1}{32} \left (1135-1772 x-876 x^2-240 x^3-1078 \log (1-2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 23, normalized size = 0.77
method | result | size |
default | \(-\frac {15 x^{3}}{2}-\frac {219 x^{2}}{8}-\frac {443 x}{8}-\frac {539 \ln \left (-1+2 x \right )}{16}\) | \(23\) |
norman | \(-\frac {15 x^{3}}{2}-\frac {219 x^{2}}{8}-\frac {443 x}{8}-\frac {539 \ln \left (-1+2 x \right )}{16}\) | \(23\) |
risch | \(-\frac {15 x^{3}}{2}-\frac {219 x^{2}}{8}-\frac {443 x}{8}-\frac {539 \ln \left (-1+2 x \right )}{16}\) | \(23\) |
meijerg | \(-\frac {539 \ln \left (1-2 x \right )}{16}-28 x -\frac {29 x \left (6 x +6\right )}{8}-\frac {15 x \left (16 x^{2}+12 x +12\right )}{32}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 22, normalized size = 0.73 \begin {gather*} -\frac {15}{2} \, x^{3} - \frac {219}{8} \, x^{2} - \frac {443}{8} \, x - \frac {539}{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 = 0.47, size = 22, normalized size = 0.73 \begin {gather*} -\frac {15}{2} \, x^{3} - \frac {219}{8} \, x^{2} - \frac {443}{8} \, x - \frac {539}{16} \, \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 = 0.03, size = 29, normalized size = 0.97 \begin {gather*} - \frac {15 x^{3}}{2} - \frac {219 x^{2}}{8} - \frac {443 x}{8} - \frac {539 \log {\left (2 x - 1 \right )}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.68, size = 23, normalized size = 0.77 \begin {gather*} -\frac {15}{2} \, x^{3} - \frac {219}{8} \, x^{2} - \frac {443}{8} \, x - \frac {539}{16} \, \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 = 20, normalized size = 0.67 \begin {gather*} -\frac {443\,x}{8}-\frac {539\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {219\,x^2}{8}-\frac {15\,x^3}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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