Optimal. Leaf size=65 \[ \frac {16807}{21296 (1-2 x)^2}-\frac {36015}{29282 (1-2 x)}-\frac {1}{332750 (3+5 x)^2}-\frac {171}{1830125 (3+5 x)}-\frac {313845 \log (1-2 x)}{1288408}+\frac {11904 \log (3+5 x)}{20131375} \]
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Rubi [A]
time = 0.02, antiderivative size = 65, 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 {36015}{29282 (1-2 x)}-\frac {171}{1830125 (5 x+3)}+\frac {16807}{21296 (1-2 x)^2}-\frac {1}{332750 (5 x+3)^2}-\frac {313845 \log (1-2 x)}{1288408}+\frac {11904 \log (5 x+3)}{20131375} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {16807}{5324 (-1+2 x)^3}-\frac {36015}{14641 (-1+2 x)^2}-\frac {313845}{644204 (-1+2 x)}+\frac {1}{33275 (3+5 x)^3}+\frac {171}{366025 (3+5 x)^2}+\frac {11904}{4026275 (3+5 x)}\right ) \, dx\\ &=\frac {16807}{21296 (1-2 x)^2}-\frac {36015}{29282 (1-2 x)}-\frac {1}{332750 (3+5 x)^2}-\frac {171}{1830125 (3+5 x)}-\frac {313845 \log (1-2 x)}{1288408}+\frac {11904 \log (3+5 x)}{20131375}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 50, normalized size = 0.77 \begin {gather*} \frac {\frac {11 \left (-116156671+261128254 x+1838287161 x^2+1800695280 x^3\right )}{\left (-3+x+10 x^2\right )^2}-78461250 \log (3-6 x)+190464 \log (-3 (3+5 x))}{322102000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 54, normalized size = 0.83
method | result | size |
risch | \(\frac {\frac {22508691}{366025} x^{3}+\frac {1838287161}{29282000} x^{2}+\frac {130564127}{14641000} x -\frac {116156671}{29282000}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {313845 \ln \left (-1+2 x \right )}{1288408}+\frac {11904 \ln \left (3+5 x \right )}{20131375}\) | \(49\) |
norman | \(\frac {-\frac {218842201}{8784600} x^{2}+\frac {130564127}{878460} x^{4}+\frac {400668419}{4392300} x^{3}+\frac {27553571}{2928200}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {313845 \ln \left (-1+2 x \right )}{1288408}+\frac {11904 \ln \left (3+5 x \right )}{20131375}\) | \(50\) |
default | \(\frac {16807}{21296 \left (-1+2 x \right )^{2}}+\frac {36015}{29282 \left (-1+2 x \right )}-\frac {313845 \ln \left (-1+2 x \right )}{1288408}-\frac {1}{332750 \left (3+5 x \right )^{2}}-\frac {171}{1830125 \left (3+5 x \right )}+\frac {11904 \ln \left (3+5 x \right )}{20131375}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 56, normalized size = 0.86 \begin {gather*} \frac {1800695280 \, x^{3} + 1838287161 \, x^{2} + 261128254 \, x - 116156671}{29282000 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {11904}{20131375} \, \log \left (5 \, x + 3\right ) - \frac {313845}{1288408} \, \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 = 1.02, size = 95, normalized size = 1.46 \begin {gather*} \frac {19807648080 \, x^{3} + 20221158771 \, x^{2} + 190464 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 78461250 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 2872410794 \, x - 1277723381}{322102000 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 54, normalized size = 0.83 \begin {gather*} - \frac {- 1800695280 x^{3} - 1838287161 x^{2} - 261128254 x + 116156671}{2928200000 x^{4} + 585640000 x^{3} - 1727638000 x^{2} - 175692000 x + 263538000} - \frac {313845 \log {\left (x - \frac {1}{2} \right )}}{1288408} + \frac {11904 \log {\left (x + \frac {3}{5} \right )}}{20131375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.60, size = 50, normalized size = 0.77 \begin {gather*} \frac {1800695280 \, x^{3} + 1838287161 \, x^{2} + 261128254 \, x - 116156671}{29282000 \, {\left (5 \, x + 3\right )}^{2} {\left (2 \, x - 1\right )}^{2}} + \frac {11904}{20131375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {313845}{1288408} \, \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 = 0.10, size = 49, normalized size = 0.75 \begin {gather*} \frac {11904\,\ln \left (x+\frac {3}{5}\right )}{20131375}-\frac {313845\,\ln \left (x-\frac {1}{2}\right )}{1288408}+\frac {\frac {22508691\,x^3}{36602500}+\frac {1838287161\,x^2}{2928200000}+\frac {130564127\,x}{1464100000}-\frac {116156671}{2928200000}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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