Optimal. Leaf size=73 \[ \frac{486 x^6}{125}+\frac{17496 x^5}{3125}-\frac{23571 x^4}{12500}-\frac{16299 x^3}{3125}+\frac{189 x^2}{15625}+\frac{920502 x}{390625}-\frac{2134}{1953125 (5 x+3)}-\frac{121}{3906250 (5 x+3)^2}+\frac{15547 \log (5 x+3)}{1953125} \]
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Rubi [A] time = 0.0368732, antiderivative size = 73, 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} \[ \frac{486 x^6}{125}+\frac{17496 x^5}{3125}-\frac{23571 x^4}{12500}-\frac{16299 x^3}{3125}+\frac{189 x^2}{15625}+\frac{920502 x}{390625}-\frac{2134}{1953125 (5 x+3)}-\frac{121}{3906250 (5 x+3)^2}+\frac{15547 \log (5 x+3)}{1953125} \]
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)^3} \, dx &=\int \left (\frac{920502}{390625}+\frac{378 x}{15625}-\frac{48897 x^2}{3125}-\frac{23571 x^3}{3125}+\frac{17496 x^4}{625}+\frac{2916 x^5}{125}+\frac{121}{390625 (3+5 x)^3}+\frac{2134}{390625 (3+5 x)^2}+\frac{15547}{390625 (3+5 x)}\right ) \, dx\\ &=\frac{920502 x}{390625}+\frac{189 x^2}{15625}-\frac{16299 x^3}{3125}-\frac{23571 x^4}{12500}+\frac{17496 x^5}{3125}+\frac{486 x^6}{125}-\frac{121}{3906250 (3+5 x)^2}-\frac{2134}{1953125 (3+5 x)}+\frac{15547 \log (3+5 x)}{1953125}\\ \end{align*}
Mathematica [A] time = 0.0351464, size = 68, normalized size = 0.93 \[ \frac{3796875000 x^8+10023750000 x^7+6086390625 x^6-5334918750 x^5-6763246875 x^4+481792500 x^3+3528738675 x^2+1743814610 x+310940 (5 x+3)^2 \log (6 (5 x+3))+274543613}{39062500 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 56, normalized size = 0.8 \begin{align*}{\frac{920502\,x}{390625}}+{\frac{189\,{x}^{2}}{15625}}-{\frac{16299\,{x}^{3}}{3125}}-{\frac{23571\,{x}^{4}}{12500}}+{\frac{17496\,{x}^{5}}{3125}}+{\frac{486\,{x}^{6}}{125}}-{\frac{121}{3906250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{2134}{5859375+9765625\,x}}+{\frac{15547\,\ln \left ( 3+5\,x \right ) }{1953125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.2008, size = 76, normalized size = 1.04 \begin{align*} \frac{486}{125} \, x^{6} + \frac{17496}{3125} \, x^{5} - \frac{23571}{12500} \, x^{4} - \frac{16299}{3125} \, x^{3} + \frac{189}{15625} \, x^{2} + \frac{920502}{390625} \, x - \frac{11 \,{\left (388 \, x + 235\right )}}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{15547}{1953125} \, \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 = 1.33263, size = 282, normalized size = 3.86 \begin{align*} \frac{759375000 \, x^{8} + 2004750000 \, x^{7} + 1217278125 \, x^{6} - 1066983750 \, x^{5} - 1352649375 \, x^{4} + 96358500 \, x^{3} + 553151700 \, x^{2} + 62188 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 165647680 \, x - 25850}{7812500 \,{\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 = 0.128251, size = 63, normalized size = 0.86 \begin{align*} \frac{486 x^{6}}{125} + \frac{17496 x^{5}}{3125} - \frac{23571 x^{4}}{12500} - \frac{16299 x^{3}}{3125} + \frac{189 x^{2}}{15625} + \frac{920502 x}{390625} - \frac{4268 x + 2585}{19531250 x^{2} + 23437500 x + 7031250} + \frac{15547 \log{\left (5 x + 3 \right )}}{1953125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.49676, size = 70, normalized size = 0.96 \begin{align*} \frac{486}{125} \, x^{6} + \frac{17496}{3125} \, x^{5} - \frac{23571}{12500} \, x^{4} - \frac{16299}{3125} \, x^{3} + \frac{189}{15625} \, x^{2} + \frac{920502}{390625} \, x - \frac{11 \,{\left (388 \, x + 235\right )}}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{15547}{1953125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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