Optimal. Leaf size=68 \[ -\frac {40089855591 x}{10000000}-\frac {7136193339 x^2}{2000000}-\frac {345533877 x^3}{100000}-\frac {111146499 x^4}{40000}-\frac {8018271 x^5}{5000}-\frac {114453 x^6}{200}-\frac {6561 x^7}{70}-\frac {5764801 \log (1-2 x)}{2816}+\frac {\log (3+5 x)}{4296875} \]
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Rubi [A]
time = 0.02, antiderivative size = 68, 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 = {84}
\begin {gather*} -\frac {6561 x^7}{70}-\frac {114453 x^6}{200}-\frac {8018271 x^5}{5000}-\frac {111146499 x^4}{40000}-\frac {345533877 x^3}{100000}-\frac {7136193339 x^2}{2000000}-\frac {40089855591 x}{10000000}-\frac {5764801 \log (1-2 x)}{2816}+\frac {\log (5 x+3)}{4296875} \end {gather*}
Antiderivative was successfully verified.
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Rule 84
Rubi steps
\begin {align*} \int \frac {(2+3 x)^8}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac {40089855591}{10000000}-\frac {7136193339 x}{1000000}-\frac {1036601631 x^2}{100000}-\frac {111146499 x^3}{10000}-\frac {8018271 x^4}{1000}-\frac {343359 x^5}{100}-\frac {6561 x^6}{10}-\frac {5764801}{1408 (-1+2 x)}+\frac {1}{859375 (3+5 x)}\right ) \, dx\\ &=-\frac {40089855591 x}{10000000}-\frac {7136193339 x^2}{2000000}-\frac {345533877 x^3}{100000}-\frac {111146499 x^4}{40000}-\frac {8018271 x^5}{5000}-\frac {114453 x^6}{200}-\frac {6561 x^7}{70}-\frac {5764801 \log (1-2 x)}{2816}+\frac {\log (3+5 x)}{4296875}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 62, normalized size = 0.91 \begin {gather*} -\frac {3 \left (40324556806+93542996379 x+83255588955 x^2+80624571300 x^3+64835457750 x^4+37418598000 x^5+13352850000 x^6+2187000000 x^7\right )}{70000000}-\frac {5764801 \log (3-6 x)}{2816}+\frac {\log (-3 (3+5 x))}{4296875} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 51, normalized size = 0.75
method | result | size |
default | \(-\frac {6561 x^{7}}{70}-\frac {114453 x^{6}}{200}-\frac {8018271 x^{5}}{5000}-\frac {111146499 x^{4}}{40000}-\frac {345533877 x^{3}}{100000}-\frac {7136193339 x^{2}}{2000000}-\frac {40089855591 x}{10000000}-\frac {5764801 \ln \left (-1+2 x \right )}{2816}+\frac {\ln \left (3+5 x \right )}{4296875}\) | \(51\) |
norman | \(-\frac {6561 x^{7}}{70}-\frac {114453 x^{6}}{200}-\frac {8018271 x^{5}}{5000}-\frac {111146499 x^{4}}{40000}-\frac {345533877 x^{3}}{100000}-\frac {7136193339 x^{2}}{2000000}-\frac {40089855591 x}{10000000}-\frac {5764801 \ln \left (-1+2 x \right )}{2816}+\frac {\ln \left (3+5 x \right )}{4296875}\) | \(51\) |
risch | \(-\frac {6561 x^{7}}{70}-\frac {114453 x^{6}}{200}-\frac {8018271 x^{5}}{5000}-\frac {111146499 x^{4}}{40000}-\frac {345533877 x^{3}}{100000}-\frac {7136193339 x^{2}}{2000000}-\frac {40089855591 x}{10000000}-\frac {5764801 \ln \left (-1+2 x \right )}{2816}+\frac {\ln \left (3+5 x \right )}{4296875}\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 50, normalized size = 0.74 \begin {gather*} -\frac {6561}{70} \, x^{7} - \frac {114453}{200} \, x^{6} - \frac {8018271}{5000} \, x^{5} - \frac {111146499}{40000} \, x^{4} - \frac {345533877}{100000} \, x^{3} - \frac {7136193339}{2000000} \, x^{2} - \frac {40089855591}{10000000} \, x + \frac {1}{4296875} \, \log \left (5 \, x + 3\right ) - \frac {5764801}{2816} \, \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 = 0.54, size = 50, normalized size = 0.74 \begin {gather*} -\frac {6561}{70} \, x^{7} - \frac {114453}{200} \, x^{6} - \frac {8018271}{5000} \, x^{5} - \frac {111146499}{40000} \, x^{4} - \frac {345533877}{100000} \, x^{3} - \frac {7136193339}{2000000} \, x^{2} - \frac {40089855591}{10000000} \, x + \frac {1}{4296875} \, \log \left (5 \, x + 3\right ) - \frac {5764801}{2816} \, \log \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 = 63, normalized size = 0.93 \begin {gather*} - \frac {6561 x^{7}}{70} - \frac {114453 x^{6}}{200} - \frac {8018271 x^{5}}{5000} - \frac {111146499 x^{4}}{40000} - \frac {345533877 x^{3}}{100000} - \frac {7136193339 x^{2}}{2000000} - \frac {40089855591 x}{10000000} - \frac {5764801 \log {\left (x - \frac {1}{2} \right )}}{2816} + \frac {\log {\left (x + \frac {3}{5} \right )}}{4296875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.66, size = 52, normalized size = 0.76 \begin {gather*} -\frac {6561}{70} \, x^{7} - \frac {114453}{200} \, x^{6} - \frac {8018271}{5000} \, x^{5} - \frac {111146499}{40000} \, x^{4} - \frac {345533877}{100000} \, x^{3} - \frac {7136193339}{2000000} \, x^{2} - \frac {40089855591}{10000000} \, x + \frac {1}{4296875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {5764801}{2816} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 46, normalized size = 0.68 \begin {gather*} \frac {\ln \left (x+\frac {3}{5}\right )}{4296875}-\frac {5764801\,\ln \left (x-\frac {1}{2}\right )}{2816}-\frac {40089855591\,x}{10000000}-\frac {7136193339\,x^2}{2000000}-\frac {345533877\,x^3}{100000}-\frac {111146499\,x^4}{40000}-\frac {8018271\,x^5}{5000}-\frac {114453\,x^6}{200}-\frac {6561\,x^7}{70} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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