Optimal. Leaf size=76 \[ \frac {5764801}{5632 (1-2 x)^2}-\frac {188591347}{30976 (1-2 x)}-\frac {2941619571 x}{400000}-\frac {110180817 x^2}{40000}-\frac {124416 x^3}{125}-\frac {408969 x^4}{1600}-\frac {6561 x^5}{200}-\frac {2644396573 \log (1-2 x)}{340736}+\frac {\log (3+5 x)}{20796875} \]
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Rubi [A]
time = 0.03, antiderivative size = 76, 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 {6561 x^5}{200}-\frac {408969 x^4}{1600}-\frac {124416 x^3}{125}-\frac {110180817 x^2}{40000}-\frac {2941619571 x}{400000}-\frac {188591347}{30976 (1-2 x)}+\frac {5764801}{5632 (1-2 x)^2}-\frac {2644396573 \log (1-2 x)}{340736}+\frac {\log (5 x+3)}{20796875} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^8}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac {2941619571}{400000}-\frac {110180817 x}{20000}-\frac {373248 x^2}{125}-\frac {408969 x^3}{400}-\frac {6561 x^4}{40}-\frac {5764801}{1408 (-1+2 x)^3}-\frac {188591347}{15488 (-1+2 x)^2}-\frac {2644396573}{170368 (-1+2 x)}+\frac {1}{4159375 (3+5 x)}\right ) \, dx\\ &=\frac {5764801}{5632 (1-2 x)^2}-\frac {188591347}{30976 (1-2 x)}-\frac {2941619571 x}{400000}-\frac {110180817 x^2}{40000}-\frac {124416 x^3}{125}-\frac {408969 x^4}{1600}-\frac {6561 x^5}{200}-\frac {2644396573 \log (1-2 x)}{340736}+\frac {\log (3+5 x)}{20796875}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 98, normalized size = 1.29 \begin {gather*} \frac {5764801}{5632 (1-2 x)^2}+\frac {188591347}{30976 (-1+2 x)}-\frac {631722537 (2+3 x)}{400000}-\frac {5992353 (2+3 x)^2}{40000}-\frac {17019 (2+3 x)^3}{1000}-\frac {2889 (2+3 x)^4}{1600}-\frac {27}{200} (2+3 x)^5-\frac {2644396573 \log (3-6 x)}{340736}+\frac {\log (-3 (3+5 x))}{20796875} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 59, normalized size = 0.78
method | result | size |
risch | \(-\frac {6561 x^{5}}{200}-\frac {408969 x^{4}}{1600}-\frac {124416 x^{3}}{125}-\frac {110180817 x^{2}}{40000}-\frac {2941619571 x}{400000}+\frac {\frac {188591347 x}{15488}-\frac {313769883}{61952}}{\left (-1+2 x \right )^{2}}-\frac {2644396573 \ln \left (-1+2 x \right )}{340736}+\frac {\ln \left (3+5 x \right )}{20796875}\) | \(55\) |
default | \(-\frac {6561 x^{5}}{200}-\frac {408969 x^{4}}{1600}-\frac {124416 x^{3}}{125}-\frac {110180817 x^{2}}{40000}-\frac {2941619571 x}{400000}+\frac {5764801}{5632 \left (-1+2 x \right )^{2}}+\frac {188591347}{30976 \left (-1+2 x \right )}-\frac {2644396573 \ln \left (-1+2 x \right )}{340736}+\frac {\ln \left (3+5 x \right )}{20796875}\) | \(59\) |
norman | \(\frac {-\frac {747118893091}{48400000} x +\frac {2270955968169}{48400000} x^{2}-\frac {1939344201}{100000} x^{3}-\frac {291695013}{40000} x^{4}-\frac {5983389}{2000} x^{5}-\frac {356481}{400} x^{6}-\frac {6561}{50} x^{7}}{\left (-1+2 x \right )^{2}}-\frac {2644396573 \ln \left (-1+2 x \right )}{340736}+\frac {\ln \left (3+5 x \right )}{20796875}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 59, normalized size = 0.78 \begin {gather*} -\frac {6561}{200} \, x^{5} - \frac {408969}{1600} \, x^{4} - \frac {124416}{125} \, x^{3} - \frac {110180817}{40000} \, x^{2} - \frac {2941619571}{400000} \, x + \frac {823543 \, {\left (916 \, x - 381\right )}}{61952 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {1}{20796875} \, \log \left (5 \, x + 3\right ) - \frac {2644396573}{340736} \, \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 = 0.43, size = 85, normalized size = 1.12 \begin {gather*} -\frac {1397230560000 \, x^{7} + 9489524220000 \, x^{6} + 31855563036000 \, x^{5} + 77649212460600 \, x^{4} + 206501370522480 \, x^{3} - 283893518434680 \, x^{2} - 512 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) + 82637392906250 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 51350638082480 \, x + 53929198640625}{10648000000 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 65, normalized size = 0.86 \begin {gather*} - \frac {6561 x^{5}}{200} - \frac {408969 x^{4}}{1600} - \frac {124416 x^{3}}{125} - \frac {110180817 x^{2}}{40000} - \frac {2941619571 x}{400000} - \frac {313769883 - 754365388 x}{247808 x^{2} - 247808 x + 61952} - \frac {2644396573 \log {\left (x - \frac {1}{2} \right )}}{340736} + \frac {\log {\left (x + \frac {3}{5} \right )}}{20796875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.34, size = 56, normalized size = 0.74 \begin {gather*} -\frac {6561}{200} \, x^{5} - \frac {408969}{1600} \, x^{4} - \frac {124416}{125} \, x^{3} - \frac {110180817}{40000} \, x^{2} - \frac {2941619571}{400000} \, x + \frac {823543 \, {\left (916 \, x - 381\right )}}{61952 \, {\left (2 \, x - 1\right )}^{2}} + \frac {1}{20796875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {2644396573}{340736} \, \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 = 0.05, size = 52, normalized size = 0.68 \begin {gather*} \frac {\ln \left (x+\frac {3}{5}\right )}{20796875}-\frac {2644396573\,\ln \left (x-\frac {1}{2}\right )}{340736}-\frac {2941619571\,x}{400000}+\frac {\frac {188591347\,x}{61952}-\frac {313769883}{247808}}{x^2-x+\frac {1}{4}}-\frac {110180817\,x^2}{40000}-\frac {124416\,x^3}{125}-\frac {408969\,x^4}{1600}-\frac {6561\,x^5}{200} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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