Optimal. Leaf size=44 \[ -\frac {1593 x}{500}-\frac {81 x^2}{100}-\frac {1}{6875 (3+5 x)}-\frac {2401}{968} \log (1-2 x)+\frac {134 \log (3+5 x)}{75625} \]
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Rubi [A]
time = 0.01, antiderivative size = 44, 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 {81 x^2}{100}-\frac {1593 x}{500}-\frac {1}{6875 (5 x+3)}-\frac {2401}{968} \log (1-2 x)+\frac {134 \log (5 x+3)}{75625} \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) (3+5 x)^2} \, dx &=\int \left (-\frac {1593}{500}-\frac {81 x}{50}-\frac {2401}{484 (-1+2 x)}+\frac {1}{1375 (3+5 x)^2}+\frac {134}{15125 (3+5 x)}\right ) \, dx\\ &=-\frac {1593 x}{500}-\frac {81 x^2}{100}-\frac {1}{6875 (3+5 x)}-\frac {2401}{968} \log (1-2 x)+\frac {134 \log (3+5 x)}{75625}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 52, normalized size = 1.18 \begin {gather*} \frac {999}{500} (1-2 x)-\frac {81}{400} (1-2 x)^2-\frac {1}{6875 (3+5 x)}-\frac {2401}{968} \log (1-2 x)+\frac {134 \log (6+10 x)}{75625} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 35, normalized size = 0.80
method | result | size |
risch | \(-\frac {81 x^{2}}{100}-\frac {1593 x}{500}-\frac {1}{34375 \left (x +\frac {3}{5}\right )}-\frac {2401 \ln \left (-1+2 x \right )}{968}+\frac {134 \ln \left (3+5 x \right )}{75625}\) | \(33\) |
default | \(-\frac {81 x^{2}}{100}-\frac {1593 x}{500}-\frac {2401 \ln \left (-1+2 x \right )}{968}-\frac {1}{6875 \left (3+5 x \right )}+\frac {134 \ln \left (3+5 x \right )}{75625}\) | \(35\) |
norman | \(\frac {-\frac {157703}{16500} x -\frac {459}{25} x^{2}-\frac {81}{20} x^{3}}{3+5 x}-\frac {2401 \ln \left (-1+2 x \right )}{968}+\frac {134 \ln \left (3+5 x \right )}{75625}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 34, normalized size = 0.77 \begin {gather*} -\frac {81}{100} \, x^{2} - \frac {1593}{500} \, x - \frac {1}{6875 \, {\left (5 \, x + 3\right )}} + \frac {134}{75625} \, \log \left (5 \, x + 3\right ) - \frac {2401}{968} \, \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 = 0.99, size = 50, normalized size = 1.14 \begin {gather*} -\frac {2450250 \, x^{3} + 11107800 \, x^{2} - 1072 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 1500625 \, {\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 5782590 \, x + 88}{605000 \, {\left (5 \, 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 = 37, normalized size = 0.84 \begin {gather*} - \frac {81 x^{2}}{100} - \frac {1593 x}{500} - \frac {2401 \log {\left (x - \frac {1}{2} \right )}}{968} + \frac {134 \log {\left (x + \frac {3}{5} \right )}}{75625} - \frac {1}{34375 x + 20625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.57, size = 63, normalized size = 1.43 \begin {gather*} -\frac {27}{2500} \, {\left (5 \, x + 3\right )}^{2} {\left (\frac {41}{5 \, x + 3} + 3\right )} - \frac {1}{6875 \, {\left (5 \, x + 3\right )}} + \frac {12393}{5000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {2401}{968} \, \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 = 30, normalized size = 0.68 \begin {gather*} \frac {134\,\ln \left (x+\frac {3}{5}\right )}{75625}-\frac {2401\,\ln \left (x-\frac {1}{2}\right )}{968}-\frac {1593\,x}{500}-\frac {1}{34375\,\left (x+\frac {3}{5}\right )}-\frac {81\,x^2}{100} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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