Optimal. Leaf size=52 \[ -\frac{54 x^3}{125}-\frac{297 x^2}{1250}+\frac{1647 x}{3125}-\frac{26}{3125 (5 x+3)}-\frac{11}{31250 (5 x+3)^2}+\frac{114 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.0219653, antiderivative size = 52, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{54 x^3}{125}-\frac{297 x^2}{1250}+\frac{1647 x}{3125}-\frac{26}{3125 (5 x+3)}-\frac{11}{31250 (5 x+3)^2}+\frac{114 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx &=\int \left (\frac{1647}{3125}-\frac{297 x}{625}-\frac{162 x^2}{125}+\frac{11}{3125 (3+5 x)^3}+\frac{26}{625 (3+5 x)^2}+\frac{114}{625 (3+5 x)}\right ) \, dx\\ &=\frac{1647 x}{3125}-\frac{297 x^2}{1250}-\frac{54 x^3}{125}-\frac{11}{31250 (3+5 x)^2}-\frac{26}{3125 (3+5 x)}+\frac{114 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.017642, size = 51, normalized size = 0.98 \[ \frac{-67500 x^5-118125 x^4+13500 x^3+133650 x^2+87220 x+228 (5 x+3)^2 \log (5 x+3)+17192}{6250 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 41, normalized size = 0.8 \begin{align*}{\frac{1647\,x}{3125}}-{\frac{297\,{x}^{2}}{1250}}-{\frac{54\,{x}^{3}}{125}}-{\frac{11}{31250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{26}{9375+15625\,x}}+{\frac{114\,\ln \left ( 3+5\,x \right ) }{3125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05095, size = 55, normalized size = 1.06 \begin{align*} -\frac{54}{125} \, x^{3} - \frac{297}{1250} \, x^{2} + \frac{1647}{3125} \, x - \frac{1300 \, x + 791}{31250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{114}{3125} \, \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 = 1.49256, size = 186, normalized size = 3.58 \begin{align*} -\frac{337500 \, x^{5} + 590625 \, x^{4} - 67500 \, x^{3} - 427275 \, x^{2} - 1140 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 146930 \, x + 791}{31250 \,{\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 = 0.123096, size = 42, normalized size = 0.81 \begin{align*} - \frac{54 x^{3}}{125} - \frac{297 x^{2}}{1250} + \frac{1647 x}{3125} - \frac{1300 x + 791}{781250 x^{2} + 937500 x + 281250} + \frac{114 \log{\left (5 x + 3 \right )}}{3125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.65722, size = 50, normalized size = 0.96 \begin{align*} -\frac{54}{125} \, x^{3} - \frac{297}{1250} \, x^{2} + \frac{1647}{3125} \, x - \frac{1300 \, x + 791}{31250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{114}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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