Optimal. Leaf size=43 \[ \frac {7}{121 (1-2 x)}-\frac {1}{121 (3+5 x)}-\frac {37 \log (1-2 x)}{1331}+\frac {37 \log (3+5 x)}{1331} \]
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Rubi [A]
time = 0.01, antiderivative size = 43, 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 {7}{121 (1-2 x)}-\frac {1}{121 (5 x+3)}-\frac {37 \log (1-2 x)}{1331}+\frac {37 \log (5 x+3)}{1331} \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)^2} \, dx &=\int \left (\frac {14}{121 (-1+2 x)^2}-\frac {74}{1331 (-1+2 x)}+\frac {5}{121 (3+5 x)^2}+\frac {185}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {7}{121 (1-2 x)}-\frac {1}{121 (3+5 x)}-\frac {37 \log (1-2 x)}{1331}+\frac {37 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 40, normalized size = 0.93 \begin {gather*} \frac {-20-37 x}{121 \left (-3+x+10 x^2\right )}-\frac {37 \log (1-2 x)}{1331}+\frac {37 \log (3+5 x)}{1331} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 36, normalized size = 0.84
method | result | size |
default | \(-\frac {7}{121 \left (-1+2 x \right )}-\frac {37 \ln \left (-1+2 x \right )}{1331}-\frac {1}{121 \left (3+5 x \right )}+\frac {37 \ln \left (3+5 x \right )}{1331}\) | \(36\) |
risch | \(\frac {-\frac {37 x}{121}-\frac {20}{121}}{\left (3+5 x \right ) \left (-1+2 x \right )}-\frac {37 \ln \left (-1+2 x \right )}{1331}+\frac {37 \ln \left (3+5 x \right )}{1331}\) | \(39\) |
norman | \(\frac {\frac {370 x^{2}}{121}-\frac {131}{121}}{\left (3+5 x \right ) \left (-1+2 x \right )}-\frac {37 \ln \left (-1+2 x \right )}{1331}+\frac {37 \ln \left (3+5 x \right )}{1331}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 34, normalized size = 0.79 \begin {gather*} -\frac {37 \, x + 20}{121 \, {\left (10 \, x^{2} + x - 3\right )}} + \frac {37}{1331} \, \log \left (5 \, x + 3\right ) - \frac {37}{1331} \, \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 = 0.44, size = 49, normalized size = 1.14 \begin {gather*} \frac {37 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) - 37 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 407 \, x - 220}{1331 \, {\left (10 \, x^{2} + x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 36, normalized size = 0.84 \begin {gather*} \frac {- 37 x - 20}{1210 x^{2} + 121 x - 363} - \frac {37 \log {\left (x - \frac {1}{2} \right )}}{1331} + \frac {37 \log {\left (x + \frac {3}{5} \right )}}{1331} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.51, size = 40, normalized size = 0.93 \begin {gather*} -\frac {1}{121 \, {\left (5 \, x + 3\right )}} + \frac {70}{1331 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}} - \frac {37}{1331} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 26, normalized size = 0.60 \begin {gather*} \frac {74\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{1331}-\frac {\frac {37\,x}{1210}+\frac {2}{121}}{x^2+\frac {x}{10}-\frac {3}{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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