Optimal. Leaf size=69 \[ \frac {2916 x^7}{175}+\frac {4374 x^6}{125}+\frac {28917 x^5}{3125}-\frac {157599 x^4}{6250}-\frac {48771 x^3}{3125}+\frac {463086 x^2}{78125}+\frac {2777053 x}{390625}-\frac {121}{1953125 (5 x+3)}+\frac {2134 \log (5 x+3)}{1953125} \]
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Rubi [A] time = 0.04, 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} \[ \frac {2916 x^7}{175}+\frac {4374 x^6}{125}+\frac {28917 x^5}{3125}-\frac {157599 x^4}{6250}-\frac {48771 x^3}{3125}+\frac {463086 x^2}{78125}+\frac {2777053 x}{390625}-\frac {121}{1953125 (5 x+3)}+\frac {2134 \log (5 x+3)}{1953125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^6}{(3+5 x)^2} \, dx &=\int \left (\frac {2777053}{390625}+\frac {926172 x}{78125}-\frac {146313 x^2}{3125}-\frac {315198 x^3}{3125}+\frac {28917 x^4}{625}+\frac {26244 x^5}{125}+\frac {2916 x^6}{25}+\frac {121}{390625 (3+5 x)^2}+\frac {2134}{390625 (3+5 x)}\right ) \, dx\\ &=\frac {2777053 x}{390625}+\frac {463086 x^2}{78125}-\frac {48771 x^3}{3125}-\frac {157599 x^4}{6250}+\frac {28917 x^5}{3125}+\frac {4374 x^6}{125}+\frac {2916 x^7}{175}-\frac {121}{1953125 (3+5 x)}+\frac {2134 \log (3+5 x)}{1953125}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 66, normalized size = 0.96 \[ \frac {11390625000 x^8+30754687500 x^7+20677781250 x^6-13442034375 x^5-21011090625 x^4-2349191250 x^3+7291044250 x^2+3997343145 x+149380 (5 x+3) \log (6 (5 x+3))+648854027}{136718750 (5 x+3)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 62, normalized size = 0.90 \[ \frac {2278125000 \, x^{8} + 6150937500 \, x^{7} + 4135556250 \, x^{6} - 2688406875 \, x^{5} - 4202218125 \, x^{4} - 469838250 \, x^{3} + 1458208850 \, x^{2} + 29876 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 583181130 \, x - 1694}{27343750 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.89, size = 93, normalized size = 1.35 \[ -\frac {1}{136718750} \, {\left (5 \, x + 3\right )}^{7} {\left (\frac {306180}{5 \, x + 3} - \frac {404838}{{\left (5 \, x + 3\right )}^{2}} - \frac {2189565}{{\left (5 \, x + 3\right )}^{3}} - \frac {2888550}{{\left (5 \, x + 3\right )}^{4}} - \frac {2081520}{{\left (5 \, x + 3\right )}^{5}} - \frac {1088290}{{\left (5 \, x + 3\right )}^{6}} - 29160\right )} - \frac {121}{1953125 \, {\left (5 \, x + 3\right )}} - \frac {2134}{1953125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 52, normalized size = 0.75 \[ \frac {2916 x^{7}}{175}+\frac {4374 x^{6}}{125}+\frac {28917 x^{5}}{3125}-\frac {157599 x^{4}}{6250}-\frac {48771 x^{3}}{3125}+\frac {463086 x^{2}}{78125}+\frac {2777053 x}{390625}+\frac {2134 \ln \left (5 x +3\right )}{1953125}-\frac {121}{1953125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 51, normalized size = 0.74 \[ \frac {2916}{175} \, x^{7} + \frac {4374}{125} \, x^{6} + \frac {28917}{3125} \, x^{5} - \frac {157599}{6250} \, x^{4} - \frac {48771}{3125} \, x^{3} + \frac {463086}{78125} \, x^{2} + \frac {2777053}{390625} \, x - \frac {121}{1953125 \, {\left (5 \, x + 3\right )}} + \frac {2134}{1953125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 49, normalized size = 0.71 \[ \frac {2777053\,x}{390625}+\frac {2134\,\ln \left (x+\frac {3}{5}\right )}{1953125}-\frac {121}{9765625\,\left (x+\frac {3}{5}\right )}+\frac {463086\,x^2}{78125}-\frac {48771\,x^3}{3125}-\frac {157599\,x^4}{6250}+\frac {28917\,x^5}{3125}+\frac {4374\,x^6}{125}+\frac {2916\,x^7}{175} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 61, normalized size = 0.88 \[ \frac {2916 x^{7}}{175} + \frac {4374 x^{6}}{125} + \frac {28917 x^{5}}{3125} - \frac {157599 x^{4}}{6250} - \frac {48771 x^{3}}{3125} + \frac {463086 x^{2}}{78125} + \frac {2777053 x}{390625} + \frac {2134 \log {\left (5 x + 3 \right )}}{1953125} - \frac {121}{9765625 x + 5859375} \]
Verification of antiderivative is not currently implemented for this CAS.
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