Optimal. Leaf size=65 \[ \frac {1331}{2401 (1-2 x)}+\frac {1}{1323 (2+3 x)^3}-\frac {101}{6174 (2+3 x)^2}+\frac {363}{2401 (2+3 x)}-\frac {3267 \log (1-2 x)}{16807}+\frac {3267 \log (2+3 x)}{16807} \]
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Rubi [A]
time = 0.02, antiderivative size = 65, 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 {1331}{2401 (1-2 x)}+\frac {363}{2401 (3 x+2)}-\frac {101}{6174 (3 x+2)^2}+\frac {1}{1323 (3 x+2)^3}-\frac {3267 \log (1-2 x)}{16807}+\frac {3267 \log (3 x+2)}{16807} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx &=\int \left (\frac {2662}{2401 (-1+2 x)^2}-\frac {6534}{16807 (-1+2 x)}-\frac {1}{147 (2+3 x)^4}+\frac {101}{1029 (2+3 x)^3}-\frac {1089}{2401 (2+3 x)^2}+\frac {9801}{16807 (2+3 x)}\right ) \, dx\\ &=\frac {1331}{2401 (1-2 x)}+\frac {1}{1323 (2+3 x)^3}-\frac {101}{6174 (2+3 x)^2}+\frac {363}{2401 (2+3 x)}-\frac {3267 \log (1-2 x)}{16807}+\frac {3267 \log (2+3 x)}{16807}\\ \end {align*}
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Mathematica [A]
time = 0.04, size = 62, normalized size = 0.95 \begin {gather*} \frac {\frac {7}{2} \left (\frac {71874}{1-2 x}+\frac {98}{(2+3 x)^3}-\frac {2121}{(2+3 x)^2}+\frac {19602}{2+3 x}\right )-88209 \log (1-2 x)+88209 \log (4+6 x)}{453789} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 54, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {29403}{2401} x^{3}-\frac {199994}{7203} x^{2}-\frac {2667797}{129654} x -\frac {324628}{64827}}{\left (-1+2 x \right ) \left (2+3 x \right )^{3}}-\frac {3267 \ln \left (-1+2 x \right )}{16807}+\frac {3267 \ln \left (2+3 x \right )}{16807}\) | \(49\) |
norman | \(\frac {-\frac {302277}{4802} x^{3}-\frac {81157}{2401} x^{4}-\frac {93717}{2401} x^{2}-\frac {38691}{4802} x}{\left (-1+2 x \right ) \left (2+3 x \right )^{3}}-\frac {3267 \ln \left (-1+2 x \right )}{16807}+\frac {3267 \ln \left (2+3 x \right )}{16807}\) | \(52\) |
default | \(-\frac {1331}{2401 \left (-1+2 x \right )}-\frac {3267 \ln \left (-1+2 x \right )}{16807}+\frac {1}{1323 \left (2+3 x \right )^{3}}-\frac {101}{6174 \left (2+3 x \right )^{2}}+\frac {363}{2401 \left (2+3 x \right )}+\frac {3267 \ln \left (2+3 x \right )}{16807}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 56, normalized size = 0.86 \begin {gather*} -\frac {1587762 \, x^{3} + 3599892 \, x^{2} + 2667797 \, x + 649256}{129654 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac {3267}{16807} \, \log \left (3 \, x + 2\right ) - \frac {3267}{16807} \, \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 = 0.41, size = 95, normalized size = 1.46 \begin {gather*} -\frac {11114334 \, x^{3} + 25199244 \, x^{2} - 176418 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 176418 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 18674579 \, x + 4544792}{907578 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\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 = 0.86 \begin {gather*} \frac {- 1587762 x^{3} - 3599892 x^{2} - 2667797 x - 649256}{7001316 x^{4} + 10501974 x^{3} + 2333772 x^{2} - 2593080 x - 1037232} - \frac {3267 \log {\left (x - \frac {1}{2} \right )}}{16807} + \frac {3267 \log {\left (x + \frac {2}{3} \right )}}{16807} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.66, size = 60, normalized size = 0.92 \begin {gather*} -\frac {1331}{2401 \, {\left (2 \, x - 1\right )}} - \frac {2 \, {\left (\frac {43645}{2 \, x - 1} + \frac {50127}{{\left (2 \, x - 1\right )}^{2}} + 9502\right )}}{16807 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{3}} + \frac {3267}{16807} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.18, size = 46, normalized size = 0.71 \begin {gather*} \frac {6534\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{16807}-\frac {\frac {1089\,x^3}{4802}+\frac {99997\,x^2}{194481}+\frac {2667797\,x}{7001316}+\frac {162314}{1750329}}{x^4+\frac {3\,x^3}{2}+\frac {x^2}{3}-\frac {10\,x}{27}-\frac {4}{27}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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