Optimal. Leaf size=54 \[ \frac {2401}{5324 (1-2 x)}-\frac {1}{30250 (3+5 x)^2}-\frac {136}{166375 (3+5 x)}+\frac {9261 \log (1-2 x)}{58564}+\frac {7074 \log (3+5 x)}{1830125} \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {2401}{5324 (1-2 x)}-\frac {136}{166375 (5 x+3)}-\frac {1}{30250 (5 x+3)^2}+\frac {9261 \log (1-2 x)}{58564}+\frac {7074 \log (5 x+3)}{1830125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4}{(1-2 x)^2 (3+5 x)^3} \, dx &=\int \left (\frac {2401}{2662 (-1+2 x)^2}+\frac {9261}{29282 (-1+2 x)}+\frac {1}{3025 (3+5 x)^3}+\frac {136}{33275 (3+5 x)^2}+\frac {7074}{366025 (3+5 x)}\right ) \, dx\\ &=\frac {2401}{5324 (1-2 x)}-\frac {1}{30250 (3+5 x)^2}-\frac {136}{166375 (3+5 x)}+\frac {9261 \log (1-2 x)}{58564}+\frac {7074 \log (3+5 x)}{1830125}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 48, normalized size = 0.89 \begin {gather*} \frac {\frac {3301375}{1-2 x}-\frac {242}{(3+5 x)^2}-\frac {5984}{3+5 x}+1157625 \log (1-2 x)+28296 \log (6+10 x)}{7320500} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 45, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {1501713}{133100} x^{2}-\frac {4502169}{332750} x -\frac {2699471}{665500}}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}+\frac {9261 \ln \left (-1+2 x \right )}{58564}+\frac {7074 \ln \left (3+5 x \right )}{1830125}\) | \(44\) |
default | \(-\frac {2401}{5324 \left (-1+2 x \right )}+\frac {9261 \ln \left (-1+2 x \right )}{58564}-\frac {1}{30250 \left (3+5 x \right )^{2}}-\frac {136}{166375 \left (3+5 x \right )}+\frac {7074 \ln \left (3+5 x \right )}{1830125}\) | \(45\) |
norman | \(\frac {-\frac {16205857}{598950} x^{2}-\frac {2699471}{119790} x^{3}-\frac {1621513}{199650} x}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}+\frac {9261 \ln \left (-1+2 x \right )}{58564}+\frac {7074 \ln \left (3+5 x \right )}{1830125}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.39, size = 46, normalized size = 0.85 \begin {gather*} -\frac {7508565 \, x^{2} + 9004338 \, x + 2699471}{665500 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac {7074}{1830125} \, \log \left (5 \, x + 3\right ) + \frac {9261}{58564} \, \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 = 0.41, size = 75, normalized size = 1.39 \begin {gather*} -\frac {82594215 \, x^{2} - 28296 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) - 1157625 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 99047718 \, x + 29694181}{7320500 \, {\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 = 0.09, size = 46, normalized size = 0.85 \begin {gather*} \frac {- 7508565 x^{2} - 9004338 x - 2699471}{33275000 x^{3} + 23292500 x^{2} - 7986000 x - 5989500} + \frac {9261 \log {\left (x - \frac {1}{2} \right )}}{58564} + \frac {7074 \log {\left (x + \frac {3}{5} \right )}}{1830125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.51, size = 69, normalized size = 1.28 \begin {gather*} -\frac {2401}{5324 \, {\left (2 \, x - 1\right )}} + \frac {2 \, {\left (\frac {1518}{2 \, x - 1} + 685\right )}}{366025 \, {\left (\frac {11}{2 \, x - 1} + 5\right )}^{2}} - \frac {81}{500} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {7074}{1830125} \, \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 = 1.12, size = 41, normalized size = 0.76 \begin {gather*} \frac {9261\,\ln \left (x-\frac {1}{2}\right )}{58564}+\frac {7074\,\ln \left (x+\frac {3}{5}\right )}{1830125}+\frac {\frac {1501713\,x^2}{6655000}+\frac {4502169\,x}{16637500}+\frac {2699471}{33275000}}{-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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