Optimal. Leaf size=65 \[ \frac {273}{14641 (1-2 x)}-\frac {72}{14641 (5 x+3)}+\frac {49}{2662 (1-2 x)^2}-\frac {1}{2662 (5 x+3)^2}-\frac {1509 \log (1-2 x)}{161051}+\frac {1509 \log (5 x+3)}{161051} \]
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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} \[ \frac {273}{14641 (1-2 x)}-\frac {72}{14641 (5 x+3)}+\frac {49}{2662 (1-2 x)^2}-\frac {1}{2662 (5 x+3)^2}-\frac {1509 \log (1-2 x)}{161051}+\frac {1509 \log (5 x+3)}{161051} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {98}{1331 (-1+2 x)^3}+\frac {546}{14641 (-1+2 x)^2}-\frac {3018}{161051 (-1+2 x)}+\frac {5}{1331 (3+5 x)^3}+\frac {360}{14641 (3+5 x)^2}+\frac {7545}{161051 (3+5 x)}\right ) \, dx\\ &=\frac {49}{2662 (1-2 x)^2}+\frac {273}{14641 (1-2 x)}-\frac {1}{2662 (3+5 x)^2}-\frac {72}{14641 (3+5 x)}-\frac {1509 \log (1-2 x)}{161051}+\frac {1509 \log (3+5 x)}{161051}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 48, normalized size = 0.74 \[ \frac {-\frac {11 \left (30180 x^3+4527 x^2-23774 x-9322\right )}{\left (10 x^2+x-3\right )^2}+3018 \log (-5 x-3)-3018 \log (1-2 x)}{322102} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 95, normalized size = 1.46 \[ -\frac {331980 \, x^{3} + 49797 \, x^{2} - 3018 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 3018 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 261514 \, x - 102542}{322102 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]
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 \[ -\frac {30180 \, x^{3} + 4527 \, x^{2} - 23774 \, x - 9322}{29282 \, {\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac {1509}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {1509}{161051} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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 \[ -\frac {1509 \ln \left (2 x -1\right )}{161051}+\frac {1509 \ln \left (5 x +3\right )}{161051}-\frac {1}{2662 \left (5 x +3\right )^{2}}-\frac {72}{14641 \left (5 x +3\right )}+\frac {49}{2662 \left (2 x -1\right )^{2}}-\frac {273}{14641 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 56, normalized size = 0.86 \[ -\frac {30180 \, x^{3} + 4527 \, x^{2} - 23774 \, x - 9322}{29282 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {1509}{161051} \, \log \left (5 \, x + 3\right ) - \frac {1509}{161051} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 45, normalized size = 0.69 \[ \frac {3018\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{161051}+\frac {-\frac {1509\,x^3}{146410}-\frac {4527\,x^2}{2928200}+\frac {11887\,x}{1464100}+\frac {4661}{1464100}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 54, normalized size = 0.83 \[ - \frac {30180 x^{3} + 4527 x^{2} - 23774 x - 9322}{2928200 x^{4} + 585640 x^{3} - 1727638 x^{2} - 175692 x + 263538} - \frac {1509 \log {\left (x - \frac {1}{2} \right )}}{161051} + \frac {1509 \log {\left (x + \frac {3}{5} \right )}}{161051} \]
Verification of antiderivative is not currently implemented for this CAS.
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