Optimal. Leaf size=65 \[ \frac {7}{1331 (1-2 x)^2}+\frac {144}{14641 (1-2 x)}-\frac {5}{2662 (3+5 x)^2}-\frac {195}{14641 (3+5 x)}-\frac {1110 \log (1-2 x)}{161051}+\frac {1110 \log (3+5 x)}{161051} \]
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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 {144}{14641 (1-2 x)}-\frac {195}{14641 (5 x+3)}+\frac {7}{1331 (1-2 x)^2}-\frac {5}{2662 (5 x+3)^2}-\frac {1110 \log (1-2 x)}{161051}+\frac {1110 \log (5 x+3)}{161051} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {2+3 x}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {28}{1331 (-1+2 x)^3}+\frac {288}{14641 (-1+2 x)^2}-\frac {2220}{161051 (-1+2 x)}+\frac {25}{1331 (3+5 x)^3}+\frac {975}{14641 (3+5 x)^2}+\frac {5550}{161051 (3+5 x)}\right ) \, dx\\ &=\frac {7}{1331 (1-2 x)^2}+\frac {144}{14641 (1-2 x)}-\frac {5}{2662 (3+5 x)^2}-\frac {195}{14641 (3+5 x)}-\frac {1110 \log (1-2 x)}{161051}+\frac {1110 \log (3+5 x)}{161051}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 48, normalized size = 0.74 \begin {gather*} \frac {\frac {11 \left (2753+11026 x-3330 x^2-22200 x^3\right )}{\left (-3+x+10 x^2\right )^2}-2220 \log (1-2 x)+2220 \log (3+5 x)}{322102} \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 | \(\frac {-\frac {11100}{14641} x^{3}-\frac {1665}{14641} x^{2}+\frac {5513}{14641} x +\frac {2753}{29282}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {1110 \ln \left (-1+2 x \right )}{161051}+\frac {1110 \ln \left (3+5 x \right )}{161051}\) | \(49\) |
norman | \(\frac {\frac {275650}{43923} x^{4}+\frac {21830}{43923} x^{3}-\frac {335257}{87846} x^{2}+\frac {9646}{14641}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {1110 \ln \left (-1+2 x \right )}{161051}+\frac {1110 \ln \left (3+5 x \right )}{161051}\) | \(50\) |
default | \(\frac {7}{1331 \left (-1+2 x \right )^{2}}-\frac {144}{14641 \left (-1+2 x \right )}-\frac {1110 \ln \left (-1+2 x \right )}{161051}-\frac {5}{2662 \left (3+5 x \right )^{2}}-\frac {195}{14641 \left (3+5 x \right )}+\frac {1110 \ln \left (3+5 x \right )}{161051}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 56, normalized size = 0.86 \begin {gather*} -\frac {22200 \, x^{3} + 3330 \, x^{2} - 11026 \, x - 2753}{29282 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {1110}{161051} \, \log \left (5 \, x + 3\right ) - \frac {1110}{161051} \, \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 = 0.71, size = 95, normalized size = 1.46 \begin {gather*} -\frac {244200 \, x^{3} + 36630 \, x^{2} - 2220 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2220 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 121286 \, x - 30283}{322102 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 54, normalized size = 0.83 \begin {gather*} - \frac {22200 x^{3} + 3330 x^{2} - 11026 x - 2753}{2928200 x^{4} + 585640 x^{3} - 1727638 x^{2} - 175692 x + 263538} - \frac {1110 \log {\left (x - \frac {1}{2} \right )}}{161051} + \frac {1110 \log {\left (x + \frac {3}{5} \right )}}{161051} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 46, normalized size = 0.71 \begin {gather*} -\frac {22200 \, x^{3} + 3330 \, x^{2} - 11026 \, x - 2753}{29282 \, {\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac {1110}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {1110}{161051} \, \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 = 0.04, size = 45, normalized size = 0.69 \begin {gather*} \frac {2220\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{161051}+\frac {-\frac {111\,x^3}{14641}-\frac {333\,x^2}{292820}+\frac {5513\,x}{1464100}+\frac {2753}{2928200}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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