Optimal. Leaf size=54 \[ \frac {14}{1331 (1-2 x)}-\frac {1}{242 (3+5 x)^2}-\frac {37}{1331 (3+5 x)}-\frac {144 \log (1-2 x)}{14641}+\frac {144 \log (3+5 x)}{14641} \]
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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 = {78}
\begin {gather*} \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} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
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 = 0.03, size = 47, normalized size = 0.87 \begin {gather*} \frac {-\frac {11 \left (19+936 x+1440 x^2\right )}{(-1+2 x) (3+5 x)^2}-288 \log (1-2 x)+288 \log (6+10 x)}{29282} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 45, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {720}{1331} x^{2}-\frac {468}{1331} x -\frac {19}{2662}}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}-\frac {144 \ln \left (-1+2 x \right )}{14641}+\frac {144 \ln \left (3+5 x \right )}{14641}\) | \(44\) |
default | \(-\frac {14}{1331 \left (-1+2 x \right )}-\frac {144 \ln \left (-1+2 x \right )}{14641}-\frac {1}{242 \left (3+5 x \right )^{2}}-\frac {37}{1331 \left (3+5 x \right )}+\frac {144 \ln \left (3+5 x \right )}{14641}\) | \(45\) |
norman | \(\frac {-\frac {475}{11979} x^{3}-\frac {13625}{23958} x^{2}-\frac {1366}{3993} x}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}-\frac {144 \ln \left (-1+2 x \right )}{14641}+\frac {144 \ln \left (3+5 x \right )}{14641}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 46, normalized size = 0.85 \begin {gather*} -\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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 75, normalized size = 1.39 \begin {gather*} -\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 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 46, normalized size = 0.85 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.57, size = 51, normalized size = 0.94 \begin {gather*} -\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 ) \end {gather*}
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 \begin {gather*} \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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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