Optimal. Leaf size=65 \[ -\frac {9261}{58564 (1-2 x)}-\frac {138}{366025 (5 x+3)}+\frac {2401}{10648 (1-2 x)^2}-\frac {1}{66550 (5 x+3)^2}-\frac {294 \log (1-2 x)}{161051}+\frac {294 \log (5 x+3)}{161051} \]
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Rubi [A] time = 0.03, 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 = {88} \[ -\frac {9261}{58564 (1-2 x)}-\frac {138}{366025 (5 x+3)}+\frac {2401}{10648 (1-2 x)^2}-\frac {1}{66550 (5 x+3)^2}-\frac {294 \log (1-2 x)}{161051}+\frac {294 \log (5 x+3)}{161051} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {2401}{2662 (-1+2 x)^3}-\frac {9261}{29282 (-1+2 x)^2}-\frac {588}{161051 (-1+2 x)}+\frac {1}{6655 (3+5 x)^3}+\frac {138}{73205 (3+5 x)^2}+\frac {1470}{161051 (3+5 x)}\right ) \, dx\\ &=\frac {2401}{10648 (1-2 x)^2}-\frac {9261}{58564 (1-2 x)}-\frac {1}{66550 (3+5 x)^2}-\frac {138}{366025 (3+5 x)}-\frac {294 \log (1-2 x)}{161051}+\frac {294 \log (3+5 x)}{161051}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 48, normalized size = 0.74 \[ \frac {\frac {11 \left (23130420 x^3+32722281 x^2+14259554 x+1771669\right )}{\left (10 x^2+x-3\right )^2}+58800 \log (-5 x-3)-58800 \log (1-2 x)}{32210200} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 95, normalized size = 1.46 \[ \frac {254434620 \, x^{3} + 359945091 \, x^{2} + 58800 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 58800 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 156855094 \, x + 19488359}{32210200 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 46, normalized size = 0.71 \[ \frac {23130420 \, x^{3} + 32722281 \, x^{2} + 14259554 \, x + 1771669}{2928200 \, {\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac {294}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {294}{161051} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 54, normalized size = 0.83 \[ -\frac {294 \ln \left (2 x -1\right )}{161051}+\frac {294 \ln \left (5 x +3\right )}{161051}-\frac {1}{66550 \left (5 x +3\right )^{2}}-\frac {138}{366025 \left (5 x +3\right )}+\frac {2401}{10648 \left (2 x -1\right )^{2}}+\frac {9261}{58564 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 56, normalized size = 0.86 \[ \frac {23130420 \, x^{3} + 32722281 \, x^{2} + 14259554 \, x + 1771669}{2928200 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {294}{161051} \, \log \left (5 \, x + 3\right ) - \frac {294}{161051} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.06, size = 45, normalized size = 0.69 \[ \frac {588\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{161051}+\frac {\frac {1156521\,x^3}{14641000}+\frac {32722281\,x^2}{292820000}+\frac {7129777\,x}{146410000}+\frac {1771669}{292820000}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 56, normalized size = 0.86 \[ - \frac {- 23130420 x^{3} - 32722281 x^{2} - 14259554 x - 1771669}{292820000 x^{4} + 58564000 x^{3} - 172763800 x^{2} - 17569200 x + 26353800} - \frac {294 \log {\left (x - \frac {1}{2} \right )}}{161051} + \frac {294 \log {\left (x + \frac {3}{5} \right )}}{161051} \]
Verification of antiderivative is not currently implemented for this CAS.
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