Optimal. Leaf size=48 \[ -\frac{81 x^4}{50}-\frac{261 x^3}{125}+\frac{378 x^2}{625}+\frac{5511 x}{3125}-\frac{11}{15625 (5 x+3)}+\frac{26 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.0219556, antiderivative size = 48, 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} \[ -\frac{81 x^4}{50}-\frac{261 x^3}{125}+\frac{378 x^2}{625}+\frac{5511 x}{3125}-\frac{11}{15625 (5 x+3)}+\frac{26 \log (5 x+3)}{3125} \]
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)^2} \, dx &=\int \left (\frac{5511}{3125}+\frac{756 x}{625}-\frac{783 x^2}{125}-\frac{162 x^3}{25}+\frac{11}{3125 (3+5 x)^2}+\frac{26}{625 (3+5 x)}\right ) \, dx\\ &=\frac{5511 x}{3125}+\frac{378 x^2}{625}-\frac{261 x^3}{125}-\frac{81 x^4}{50}-\frac{11}{15625 (3+5 x)}+\frac{26 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0156897, size = 49, normalized size = 1.02 \[ \frac{-50625 x^5-95625 x^4-20250 x^3+66450 x^2+51795 x+52 (5 x+3) \log (5 x+3)+11233}{6250 (5 x+3)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 37, normalized size = 0.8 \begin{align*}{\frac{5511\,x}{3125}}+{\frac{378\,{x}^{2}}{625}}-{\frac{261\,{x}^{3}}{125}}-{\frac{81\,{x}^{4}}{50}}-{\frac{11}{46875+78125\,x}}+{\frac{26\,\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 = 1.01558, size = 49, normalized size = 1.02 \begin{align*} -\frac{81}{50} \, x^{4} - \frac{261}{125} \, x^{3} + \frac{378}{625} \, x^{2} + \frac{5511}{3125} \, x - \frac{11}{15625 \,{\left (5 \, x + 3\right )}} + \frac{26}{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 = 1.56189, size = 158, normalized size = 3.29 \begin{align*} -\frac{253125 \, x^{5} + 478125 \, x^{4} + 101250 \, x^{3} - 332250 \, x^{2} - 260 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 165330 \, x + 22}{31250 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.103385, size = 41, normalized size = 0.85 \begin{align*} - \frac{81 x^{4}}{50} - \frac{261 x^{3}}{125} + \frac{378 x^{2}}{625} + \frac{5511 x}{3125} + \frac{26 \log{\left (5 x + 3 \right )}}{3125} - \frac{11}{78125 x + 46875} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.92302, size = 89, normalized size = 1.85 \begin{align*} \frac{3}{31250} \,{\left (5 \, x + 3\right )}^{4}{\left (\frac{150}{5 \, x + 3} + \frac{360}{{\left (5 \, x + 3\right )}^{2}} + \frac{380}{{\left (5 \, x + 3\right )}^{3}} - 27\right )} - \frac{11}{15625 \,{\left (5 \, x + 3\right )}} - \frac{26}{3125} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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