Optimal. Leaf size=37 \[ -\frac {3389 x}{16}-\frac {2205 x^2}{16}-\frac {279 x^3}{4}-\frac {135 x^4}{8}-\frac {3773}{32} \log (1-2 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 37, 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 {135 x^4}{8}-\frac {279 x^3}{4}-\frac {2205 x^2}{16}-\frac {3389 x}{16}-\frac {3773}{32} \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)^3 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac {3389}{16}-\frac {2205 x}{8}-\frac {837 x^2}{4}-\frac {135 x^3}{2}-\frac {3773}{16 (-1+2 x)}\right ) \, dx\\ &=-\frac {3389 x}{16}-\frac {2205 x^2}{16}-\frac {279 x^3}{4}-\frac {135 x^4}{8}-\frac {3773}{32} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 32, normalized size = 0.86 \begin {gather*} \frac {1}{128} \left (19217-27112 x-17640 x^2-8928 x^3-2160 x^4-15092 \log (1-2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 28, normalized size = 0.76
method | result | size |
default | \(-\frac {135 x^{4}}{8}-\frac {279 x^{3}}{4}-\frac {2205 x^{2}}{16}-\frac {3389 x}{16}-\frac {3773 \ln \left (-1+2 x \right )}{32}\) | \(28\) |
norman | \(-\frac {135 x^{4}}{8}-\frac {279 x^{3}}{4}-\frac {2205 x^{2}}{16}-\frac {3389 x}{16}-\frac {3773 \ln \left (-1+2 x \right )}{32}\) | \(28\) |
risch | \(-\frac {135 x^{4}}{8}-\frac {279 x^{3}}{4}-\frac {2205 x^{2}}{16}-\frac {3389 x}{16}-\frac {3773 \ln \left (-1+2 x \right )}{32}\) | \(28\) |
meijerg | \(-\frac {3773 \ln \left (1-2 x \right )}{32}-74 x -\frac {57 x \left (6 x +6\right )}{4}-\frac {117 x \left (16 x^{2}+12 x +12\right )}{32}-\frac {9 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{64}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 27, normalized size = 0.73 \begin {gather*} -\frac {135}{8} \, x^{4} - \frac {279}{4} \, x^{3} - \frac {2205}{16} \, x^{2} - \frac {3389}{16} \, x - \frac {3773}{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 = 0.43, size = 27, normalized size = 0.73 \begin {gather*} -\frac {135}{8} \, x^{4} - \frac {279}{4} \, x^{3} - \frac {2205}{16} \, x^{2} - \frac {3389}{16} \, x - \frac {3773}{32} \, \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 = 36, normalized size = 0.97 \begin {gather*} - \frac {135 x^{4}}{8} - \frac {279 x^{3}}{4} - \frac {2205 x^{2}}{16} - \frac {3389 x}{16} - \frac {3773 \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 = 0.73, size = 28, normalized size = 0.76 \begin {gather*} -\frac {135}{8} \, x^{4} - \frac {279}{4} \, x^{3} - \frac {2205}{16} \, x^{2} - \frac {3389}{16} \, x - \frac {3773}{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 = 25, normalized size = 0.68 \begin {gather*} -\frac {3389\,x}{16}-\frac {3773\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {2205\,x^2}{16}-\frac {279\,x^3}{4}-\frac {135\,x^4}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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