Optimal. Leaf size=58 \[ \frac {117649}{704 (1-2 x)}+\frac {3946293 x}{10000}+\frac {639819 x^2}{4000}+\frac {2673 x^3}{50}+\frac {729 x^4}{80}+\frac {2739541 \log (1-2 x)}{7744}+\frac {\log (3+5 x)}{378125} \]
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Rubi [A]
time = 0.02, antiderivative size = 58, 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 {729 x^4}{80}+\frac {2673 x^3}{50}+\frac {639819 x^2}{4000}+\frac {3946293 x}{10000}+\frac {117649}{704 (1-2 x)}+\frac {2739541 \log (1-2 x)}{7744}+\frac {\log (5 x+3)}{378125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^6}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac {3946293}{10000}+\frac {639819 x}{2000}+\frac {8019 x^2}{50}+\frac {729 x^3}{20}+\frac {117649}{352 (-1+2 x)^2}+\frac {2739541}{3872 (-1+2 x)}+\frac {1}{75625 (3+5 x)}\right ) \, dx\\ &=\frac {117649}{704 (1-2 x)}+\frac {3946293 x}{10000}+\frac {639819 x^2}{4000}+\frac {2673 x^3}{50}+\frac {729 x^4}{80}+\frac {2739541 \log (1-2 x)}{7744}+\frac {\log (3+5 x)}{378125}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 55, normalized size = 0.95 \begin {gather*} \frac {\frac {55 \left (-156937135-6823872 x+276893694 x^2+117237780 x^3+43035300 x^4+8019000 x^5\right )}{-1+2 x}+8561065625 \log (5-10 x)+64 \log (3+5 x)}{24200000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 45, normalized size = 0.78
method | result | size |
risch | \(\frac {729 x^{4}}{80}+\frac {2673 x^{3}}{50}+\frac {639819 x^{2}}{4000}+\frac {3946293 x}{10000}-\frac {117649}{1408 \left (-\frac {1}{2}+x \right )}+\frac {2739541 \ln \left (-1+2 x \right )}{7744}+\frac {\ln \left (3+5 x \right )}{378125}\) | \(43\) |
default | \(\frac {729 x^{4}}{80}+\frac {2673 x^{3}}{50}+\frac {639819 x^{2}}{4000}+\frac {3946293 x}{10000}-\frac {117649}{704 \left (-1+2 x \right )}+\frac {2739541 \ln \left (-1+2 x \right )}{7744}+\frac {\ln \left (3+5 x \right )}{378125}\) | \(45\) |
norman | \(\frac {-\frac {160349071}{220000} x +\frac {12586077}{20000} x^{2}+\frac {532899}{2000} x^{3}+\frac {39123}{400} x^{4}+\frac {729}{40} x^{5}}{-1+2 x}+\frac {2739541 \ln \left (-1+2 x \right )}{7744}+\frac {\ln \left (3+5 x \right )}{378125}\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 44, normalized size = 0.76 \begin {gather*} \frac {729}{80} \, x^{4} + \frac {2673}{50} \, x^{3} + \frac {639819}{4000} \, x^{2} + \frac {3946293}{10000} \, x - \frac {117649}{704 \, {\left (2 \, x - 1\right )}} + \frac {1}{378125} \, \log \left (5 \, x + 3\right ) + \frac {2739541}{7744} \, \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 = 0.38, size = 60, normalized size = 1.03 \begin {gather*} \frac {441045000 \, x^{5} + 2366941500 \, x^{4} + 6448077900 \, x^{3} + 15229153170 \, x^{2} + 64 \, {\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 8561065625 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 9550029060 \, x - 4044184375}{24200000 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 49, normalized size = 0.84 \begin {gather*} \frac {729 x^{4}}{80} + \frac {2673 x^{3}}{50} + \frac {639819 x^{2}}{4000} + \frac {3946293 x}{10000} + \frac {2739541 \log {\left (x - \frac {1}{2} \right )}}{7744} + \frac {\log {\left (x + \frac {3}{5} \right )}}{378125} - \frac {117649}{1408 x - 704} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.67, size = 81, normalized size = 1.40 \begin {gather*} \frac {27}{160000} \, {\left (2 \, x - 1\right )}^{4} {\left (\frac {53100}{2 \, x - 1} + \frac {376020}{{\left (2 \, x - 1\right )}^{2}} + \frac {1775512}{{\left (2 \, x - 1\right )}^{3}} + 3375\right )} - \frac {117649}{704 \, {\left (2 \, x - 1\right )}} - \frac {70752609}{200000} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {1}{378125} \, \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 = 40, normalized size = 0.69 \begin {gather*} \frac {3946293\,x}{10000}+\frac {2739541\,\ln \left (x-\frac {1}{2}\right )}{7744}+\frac {\ln \left (x+\frac {3}{5}\right )}{378125}-\frac {117649}{1408\,\left (x-\frac {1}{2}\right )}+\frac {639819\,x^2}{4000}+\frac {2673\,x^3}{50}+\frac {729\,x^4}{80} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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