Optimal. Leaf size=65 \[ \frac {44}{2401 (1-2 x)}+\frac {1}{147 (2+3 x)^3}-\frac {31}{686 (2+3 x)^2}-\frac {128}{2401 (2+3 x)}-\frac {388 \log (1-2 x)}{16807}+\frac {388 \log (2+3 x)}{16807} \]
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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 = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} \frac {44}{2401 (1-2 x)}-\frac {128}{2401 (3 x+2)}-\frac {31}{686 (3 x+2)^2}+\frac {1}{147 (3 x+2)^3}-\frac {388 \log (1-2 x)}{16807}+\frac {388 \log (3 x+2)}{16807} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^2 (2+3 x)^4} \, dx &=\int \left (\frac {88}{2401 (-1+2 x)^2}-\frac {776}{16807 (-1+2 x)}-\frac {3}{49 (2+3 x)^4}+\frac {93}{343 (2+3 x)^3}+\frac {384}{2401 (2+3 x)^2}+\frac {1164}{16807 (2+3 x)}\right ) \, dx\\ &=\frac {44}{2401 (1-2 x)}+\frac {1}{147 (2+3 x)^3}-\frac {31}{686 (2+3 x)^2}-\frac {128}{2401 (2+3 x)}-\frac {388 \log (1-2 x)}{16807}+\frac {388 \log (2+3 x)}{16807}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 52, normalized size = 0.80 \begin {gather*} \frac {-\frac {7 \left (-2164+6887 x+29682 x^2+20952 x^3\right )}{(-1+2 x) (2+3 x)^3}-2328 \log (3-6 x)+2328 \log (2+3 x)}{100842} \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 | \(\frac {-\frac {3492}{2401} x^{3}-\frac {4947}{2401} x^{2}-\frac {6887}{14406} x +\frac {1082}{7203}}{\left (-1+2 x \right ) \left (2+3 x \right )^{3}}-\frac {388 \ln \left (-1+2 x \right )}{16807}+\frac {388 \ln \left (2+3 x \right )}{16807}\) | \(49\) |
norman | \(\frac {\frac {639}{9604} x^{3}+\frac {4869}{4802} x^{4}-\frac {8271}{4802} x^{2}-\frac {4099}{4802} x}{\left (-1+2 x \right ) \left (2+3 x \right )^{3}}-\frac {388 \ln \left (-1+2 x \right )}{16807}+\frac {388 \ln \left (2+3 x \right )}{16807}\) | \(52\) |
default | \(-\frac {44}{2401 \left (-1+2 x \right )}-\frac {388 \ln \left (-1+2 x \right )}{16807}+\frac {1}{147 \left (2+3 x \right )^{3}}-\frac {31}{686 \left (2+3 x \right )^{2}}-\frac {128}{2401 \left (2+3 x \right )}+\frac {388 \ln \left (2+3 x \right )}{16807}\) | \(54\) |
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 {20952 \, x^{3} + 29682 \, x^{2} + 6887 \, x - 2164}{14406 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac {388}{16807} \, \log \left (3 \, x + 2\right ) - \frac {388}{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 = 0.86, size = 95, normalized size = 1.46 \begin {gather*} -\frac {146664 \, x^{3} + 207774 \, x^{2} - 2328 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 2328 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 48209 \, x - 15148}{100842 \, {\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 = 0.08, size = 54, normalized size = 0.83 \begin {gather*} \frac {- 20952 x^{3} - 29682 x^{2} - 6887 x + 2164}{777924 x^{4} + 1166886 x^{3} + 259308 x^{2} - 288120 x - 115248} - \frac {388 \log {\left (x - \frac {1}{2} \right )}}{16807} + \frac {388 \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 = 1.41, size = 60, normalized size = 0.92 \begin {gather*} -\frac {44}{2401 \, {\left (2 \, x - 1\right )}} + \frac {18 \, {\left (\frac {2415}{2 \, x - 1} + \frac {3038}{{\left (2 \, x - 1\right )}^{2}} + 473\right )}}{16807 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{3}} + \frac {388}{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 = 1.08, size = 46, normalized size = 0.71 \begin {gather*} \frac {776\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{16807}-\frac {\frac {194\,x^3}{7203}+\frac {1649\,x^2}{43218}+\frac {6887\,x}{777924}-\frac {541}{194481}}{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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