Optimal. Leaf size=69 \[ -\frac {2187 x^4}{160}-\frac {40581 x^3}{400}-\frac {792423 x^2}{2000}-\frac {26161299 x}{20000}-\frac {5764801}{3872 (1-2 x)}+\frac {823543}{2816 (1-2 x)^2}-\frac {269063263 \log (1-2 x)}{170368}+\frac {\log (5 x+3)}{4159375} \]
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Rubi [A] time = 0.03, antiderivative size = 69, 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 = {88} \[ -\frac {2187 x^4}{160}-\frac {40581 x^3}{400}-\frac {792423 x^2}{2000}-\frac {26161299 x}{20000}-\frac {5764801}{3872 (1-2 x)}+\frac {823543}{2816 (1-2 x)^2}-\frac {269063263 \log (1-2 x)}{170368}+\frac {\log (5 x+3)}{4159375} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^7}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac {26161299}{20000}-\frac {792423 x}{1000}-\frac {121743 x^2}{400}-\frac {2187 x^3}{40}-\frac {823543}{704 (-1+2 x)^3}-\frac {5764801}{1936 (-1+2 x)^2}-\frac {269063263}{85184 (-1+2 x)}+\frac {1}{831875 (3+5 x)}\right ) \, dx\\ &=\frac {823543}{2816 (1-2 x)^2}-\frac {5764801}{3872 (1-2 x)}-\frac {26161299 x}{20000}-\frac {792423 x^2}{2000}-\frac {40581 x^3}{400}-\frac {2187 x^4}{160}-\frac {269063263 \log (1-2 x)}{170368}+\frac {\log (3+5 x)}{4159375}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 60, normalized size = 0.87 \[ \frac {-\frac {55 \left (1058508000 x^6+6797973600 x^5+23090763960 x^4+72578051568 x^3-42333890544 x^2-83615877112 x+35985148011\right )}{(1-2 x)^2}-1681645393750 \log (5-10 x)+256 \log (5 x+3)}{1064800000} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 80, normalized size = 1.16 \[ -\frac {58217940000 \, x^{6} + 373888548000 \, x^{5} + 1269992017800 \, x^{4} + 3991792836240 \, x^{3} - 5149424229840 \, x^{2} - 256 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) + 1681645393750 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1777812991240 \, x + 1273918078125}{1064800000 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 51, normalized size = 0.74 \[ -\frac {2187}{160} \, x^{4} - \frac {40581}{400} \, x^{3} - \frac {792423}{2000} \, x^{2} - \frac {26161299}{20000} \, x + \frac {823543 \, {\left (112 \, x - 45\right )}}{30976 \, {\left (2 \, x - 1\right )}^{2}} + \frac {1}{4159375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {269063263}{170368} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 54, normalized size = 0.78 \[ -\frac {2187 x^{4}}{160}-\frac {40581 x^{3}}{400}-\frac {792423 x^{2}}{2000}-\frac {26161299 x}{20000}-\frac {269063263 \ln \left (2 x -1\right )}{170368}+\frac {\ln \left (5 x +3\right )}{4159375}+\frac {823543}{2816 \left (2 x -1\right )^{2}}+\frac {5764801}{3872 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 54, normalized size = 0.78 \[ -\frac {2187}{160} \, x^{4} - \frac {40581}{400} \, x^{3} - \frac {792423}{2000} \, x^{2} - \frac {26161299}{20000} \, x + \frac {823543 \, {\left (112 \, x - 45\right )}}{30976 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {1}{4159375} \, \log \left (5 \, x + 3\right ) - \frac {269063263}{170368} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 47, normalized size = 0.68 \[ \frac {\ln \left (x+\frac {3}{5}\right )}{4159375}-\frac {269063263\,\ln \left (x-\frac {1}{2}\right )}{170368}-\frac {26161299\,x}{20000}+\frac {\frac {5764801\,x}{7744}-\frac {37059435}{123904}}{x^2-x+\frac {1}{4}}-\frac {792423\,x^2}{2000}-\frac {40581\,x^3}{400}-\frac {2187\,x^4}{160} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 58, normalized size = 0.84 \[ - \frac {2187 x^{4}}{160} - \frac {40581 x^{3}}{400} - \frac {792423 x^{2}}{2000} - \frac {26161299 x}{20000} - \frac {37059435 - 92236816 x}{123904 x^{2} - 123904 x + 30976} - \frac {269063263 \log {\left (x - \frac {1}{2} \right )}}{170368} + \frac {\log {\left (x + \frac {3}{5} \right )}}{4159375} \]
Verification of antiderivative is not currently implemented for this CAS.
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