Optimal. Leaf size=80 \[ \frac{8748 x^7}{875}+\frac{13608 x^6}{625}+\frac{104247 x^5}{15625}-\frac{193833 x^4}{12500}-\frac{162612 x^3}{15625}+\frac{1390203 x^2}{390625}+\frac{9251661 x}{1953125}-\frac{2497}{9765625 (5 x+3)}-\frac{121}{19531250 (5 x+3)^2}+\frac{21949 \log (5 x+3)}{9765625} \]
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Rubi [A] time = 0.0423137, antiderivative size = 80, normalized size of antiderivative = 1., 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} \[ \frac{8748 x^7}{875}+\frac{13608 x^6}{625}+\frac{104247 x^5}{15625}-\frac{193833 x^4}{12500}-\frac{162612 x^3}{15625}+\frac{1390203 x^2}{390625}+\frac{9251661 x}{1953125}-\frac{2497}{9765625 (5 x+3)}-\frac{121}{19531250 (5 x+3)^2}+\frac{21949 \log (5 x+3)}{9765625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx &=\int \left (\frac{9251661}{1953125}+\frac{2780406 x}{390625}-\frac{487836 x^2}{15625}-\frac{193833 x^3}{3125}+\frac{104247 x^4}{3125}+\frac{81648 x^5}{625}+\frac{8748 x^6}{125}+\frac{121}{1953125 (3+5 x)^3}+\frac{2497}{1953125 (3+5 x)^2}+\frac{21949}{1953125 (3+5 x)}\right ) \, dx\\ &=\frac{9251661 x}{1953125}+\frac{1390203 x^2}{390625}-\frac{162612 x^3}{15625}-\frac{193833 x^4}{12500}+\frac{104247 x^5}{15625}+\frac{13608 x^6}{625}+\frac{8748 x^7}{875}-\frac{121}{19531250 (3+5 x)^2}-\frac{2497}{9765625 (3+5 x)}+\frac{21949 \log (3+5 x)}{9765625}\\ \end{align*}
Mathematica [A] time = 0.0275327, size = 71, normalized size = 0.89 \[ \frac{341718750000 x^9+1154250000000 x^8+1244084062500 x^7+11543765625 x^6-909633768750 x^5-496018096875 x^4+179818432500 x^3+275860261575 x^2+103624499690 x+3072860 (5 x+3)^2 \log (5 x+3)+13601177777}{1367187500 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 61, normalized size = 0.8 \begin{align*}{\frac{9251661\,x}{1953125}}+{\frac{1390203\,{x}^{2}}{390625}}-{\frac{162612\,{x}^{3}}{15625}}-{\frac{193833\,{x}^{4}}{12500}}+{\frac{104247\,{x}^{5}}{15625}}+{\frac{13608\,{x}^{6}}{625}}+{\frac{8748\,{x}^{7}}{875}}-{\frac{121}{19531250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{2497}{29296875+48828125\,x}}+{\frac{21949\,\ln \left ( 3+5\,x \right ) }{9765625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.7805, size = 82, normalized size = 1.02 \begin{align*} \frac{8748}{875} \, x^{7} + \frac{13608}{625} \, x^{6} + \frac{104247}{15625} \, x^{5} - \frac{193833}{12500} \, x^{4} - \frac{162612}{15625} \, x^{3} + \frac{1390203}{390625} \, x^{2} + \frac{9251661}{1953125} \, x - \frac{11 \,{\left (2270 \, x + 1373\right )}}{19531250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{21949}{9765625} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.22276, size = 332, normalized size = 4.15 \begin{align*} \frac{68343750000 \, x^{9} + 230850000000 \, x^{8} + 248816812500 \, x^{7} + 2308753125 \, x^{6} - 181926753750 \, x^{5} - 99203619375 \, x^{4} + 35963686500 \, x^{3} + 47615255100 \, x^{2} + 614572 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 11656743280 \, x - 211442}{273437500 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.130017, size = 70, normalized size = 0.88 \begin{align*} \frac{8748 x^{7}}{875} + \frac{13608 x^{6}}{625} + \frac{104247 x^{5}}{15625} - \frac{193833 x^{4}}{12500} - \frac{162612 x^{3}}{15625} + \frac{1390203 x^{2}}{390625} + \frac{9251661 x}{1953125} - \frac{24970 x + 15103}{488281250 x^{2} + 585937500 x + 175781250} + \frac{21949 \log{\left (5 x + 3 \right )}}{9765625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.49997, size = 77, normalized size = 0.96 \begin{align*} \frac{8748}{875} \, x^{7} + \frac{13608}{625} \, x^{6} + \frac{104247}{15625} \, x^{5} - \frac{193833}{12500} \, x^{4} - \frac{162612}{15625} \, x^{3} + \frac{1390203}{390625} \, x^{2} + \frac{9251661}{1953125} \, x - \frac{11 \,{\left (2270 \, x + 1373\right )}}{19531250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{21949}{9765625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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