Optimal. Leaf size=54 \[ \frac {14}{1331 (1-2 x)}-\frac {37}{1331 (5 x+3)}-\frac {1}{242 (5 x+3)^2}-\frac {144 \log (1-2 x)}{14641}+\frac {144 \log (5 x+3)}{14641} \]
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Rubi [A] time = 0.02, antiderivative size = 54, 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 = {77} \[ \frac {14}{1331 (1-2 x)}-\frac {37}{1331 (5 x+3)}-\frac {1}{242 (5 x+3)^2}-\frac {144 \log (1-2 x)}{14641}+\frac {144 \log (5 x+3)}{14641} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {2+3 x}{(1-2 x)^2 (3+5 x)^3} \, dx &=\int \left (\frac {28}{1331 (-1+2 x)^2}-\frac {288}{14641 (-1+2 x)}+\frac {5}{121 (3+5 x)^3}+\frac {185}{1331 (3+5 x)^2}+\frac {720}{14641 (3+5 x)}\right ) \, dx\\ &=\frac {14}{1331 (1-2 x)}-\frac {1}{242 (3+5 x)^2}-\frac {37}{1331 (3+5 x)}-\frac {144 \log (1-2 x)}{14641}+\frac {144 \log (3+5 x)}{14641}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 47, normalized size = 0.87 \[ \frac {-\frac {11 \left (1440 x^2+936 x+19\right )}{(2 x-1) (5 x+3)^2}-288 \log (1-2 x)+288 \log (10 x+6)}{29282} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 75, normalized size = 1.39 \[ -\frac {15840 \, x^{2} - 288 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 288 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 10296 \, x + 209}{29282 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.15, size = 51, normalized size = 0.94 \[ -\frac {14}{1331 \, {\left (2 \, x - 1\right )}} + \frac {10 \, {\left (\frac {429}{2 \, x - 1} + 190\right )}}{14641 \, {\left (\frac {11}{2 \, x - 1} + 5\right )}^{2}} + \frac {144}{14641} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 45, normalized size = 0.83 \[ -\frac {144 \ln \left (2 x -1\right )}{14641}+\frac {144 \ln \left (5 x +3\right )}{14641}-\frac {1}{242 \left (5 x +3\right )^{2}}-\frac {37}{1331 \left (5 x +3\right )}-\frac {14}{1331 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 46, normalized size = 0.85 \[ -\frac {1440 \, x^{2} + 936 \, x + 19}{2662 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac {144}{14641} \, \log \left (5 \, x + 3\right ) - \frac {144}{14641} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 37, normalized size = 0.69 \[ \frac {288\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{14641}+\frac {\frac {72\,x^2}{6655}+\frac {234\,x}{33275}+\frac {19}{133100}}{-x^3-\frac {7\,x^2}{10}+\frac {6\,x}{25}+\frac {9}{50}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 46, normalized size = 0.85 \[ \frac {- 1440 x^{2} - 936 x - 19}{133100 x^{3} + 93170 x^{2} - 31944 x - 23958} - \frac {144 \log {\left (x - \frac {1}{2} \right )}}{14641} + \frac {144 \log {\left (x + \frac {3}{5} \right )}}{14641} \]
Verification of antiderivative is not currently implemented for this CAS.
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