Optimal. Leaf size=73 \[ -\frac{324 x^6}{125}-\frac{324 x^5}{3125}+\frac{22977 x^4}{6250}-\frac{393 x^3}{625}-\frac{62097 x^2}{31250}+\frac{424432 x}{390625}-\frac{19239}{1953125 (5 x+3)}-\frac{1331}{3906250 (5 x+3)^2}+\frac{109032 \log (5 x+3)}{1953125} \]
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Rubi [A] time = 0.0402849, 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} \[ -\frac{324 x^6}{125}-\frac{324 x^5}{3125}+\frac{22977 x^4}{6250}-\frac{393 x^3}{625}-\frac{62097 x^2}{31250}+\frac{424432 x}{390625}-\frac{19239}{1953125 (5 x+3)}-\frac{1331}{3906250 (5 x+3)^2}+\frac{109032 \log (5 x+3)}{1953125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (2+3 x)^5}{(3+5 x)^3} \, dx &=\int \left (\frac{424432}{390625}-\frac{62097 x}{15625}-\frac{1179 x^2}{625}+\frac{45954 x^3}{3125}-\frac{324 x^4}{625}-\frac{1944 x^5}{125}+\frac{1331}{390625 (3+5 x)^3}+\frac{19239}{390625 (3+5 x)^2}+\frac{109032}{390625 (3+5 x)}\right ) \, dx\\ &=\frac{424432 x}{390625}-\frac{62097 x^2}{31250}-\frac{393 x^3}{625}+\frac{22977 x^4}{6250}-\frac{324 x^5}{3125}-\frac{324 x^6}{125}-\frac{1331}{3906250 (3+5 x)^2}-\frac{19239}{1953125 (3+5 x)}+\frac{109032 \log (3+5 x)}{1953125}\\ \end{align*}
Mathematica [A] time = 0.0348605, size = 68, normalized size = 0.93 \[ \frac{-1265625000 x^8-1569375000 x^7+1278703125 x^6+1828837500 x^5-692475000 x^4-744310000 x^3+711123525 x^2+698557830 x+1090320 (5 x+3)^2 \log (6 (5 x+3))+151973789}{19531250 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 56, normalized size = 0.8 \begin{align*}{\frac{424432\,x}{390625}}-{\frac{62097\,{x}^{2}}{31250}}-{\frac{393\,{x}^{3}}{625}}+{\frac{22977\,{x}^{4}}{6250}}-{\frac{324\,{x}^{5}}{3125}}-{\frac{324\,{x}^{6}}{125}}-{\frac{1331}{3906250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{19239}{5859375+9765625\,x}}+{\frac{109032\,\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 = 2.38809, size = 76, normalized size = 1.04 \begin{align*} -\frac{324}{125} \, x^{6} - \frac{324}{3125} \, x^{5} + \frac{22977}{6250} \, x^{4} - \frac{393}{625} \, x^{3} - \frac{62097}{31250} \, x^{2} + \frac{424432}{390625} \, x - \frac{121 \,{\left (318 \, x + 193\right )}}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{109032}{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 = 1.2694, size = 279, normalized size = 3.82 \begin{align*} -\frac{253125000 \, x^{8} + 313875000 \, x^{7} - 255740625 \, x^{6} - 365767500 \, x^{5} + 138495000 \, x^{4} + 148862000 \, x^{3} - 57470475 \, x^{2} - 218064 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 38006490 \, x + 116765}{3906250 \,{\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 = 0.128031, size = 63, normalized size = 0.86 \begin{align*} - \frac{324 x^{6}}{125} - \frac{324 x^{5}}{3125} + \frac{22977 x^{4}}{6250} - \frac{393 x^{3}}{625} - \frac{62097 x^{2}}{31250} + \frac{424432 x}{390625} - \frac{38478 x + 23353}{19531250 x^{2} + 23437500 x + 7031250} + \frac{109032 \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 = 1.51274, size = 70, normalized size = 0.96 \begin{align*} -\frac{324}{125} \, x^{6} - \frac{324}{3125} \, x^{5} + \frac{22977}{6250} \, x^{4} - \frac{393}{625} \, x^{3} - \frac{62097}{31250} \, x^{2} + \frac{424432}{390625} \, x - \frac{121 \,{\left (318 \, x + 193\right )}}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{109032}{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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