Optimal. Leaf size=41 \[ \frac{12 x^3}{25}-\frac{78 x^2}{125}+\frac{37 x}{625}-\frac{121}{3125 (5 x+3)}+\frac{682 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.0186623, antiderivative size = 41, 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} \[ \frac{12 x^3}{25}-\frac{78 x^2}{125}+\frac{37 x}{625}-\frac{121}{3125 (5 x+3)}+\frac{682 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (2+3 x)^2}{(3+5 x)^2} \, dx &=\int \left (\frac{37}{625}-\frac{156 x}{125}+\frac{36 x^2}{25}+\frac{121}{625 (3+5 x)^2}+\frac{682}{625 (3+5 x)}\right ) \, dx\\ &=\frac{37 x}{625}-\frac{78 x^2}{125}+\frac{12 x^3}{25}-\frac{121}{3125 (3+5 x)}+\frac{682 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0160155, size = 42, normalized size = 1.02 \[ \frac{\frac{5 \left (1500 x^4-1050 x^3-985 x^2+1248 x+658\right )}{5 x+3}+682 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 32, normalized size = 0.8 \begin{align*}{\frac{37\,x}{625}}-{\frac{78\,{x}^{2}}{125}}+{\frac{12\,{x}^{3}}{25}}-{\frac{121}{9375+15625\,x}}+{\frac{682\,\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 = 1.13228, size = 42, normalized size = 1.02 \begin{align*} \frac{12}{25} \, x^{3} - \frac{78}{125} \, x^{2} + \frac{37}{625} \, x - \frac{121}{3125 \,{\left (5 \, x + 3\right )}} + \frac{682}{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 = 1.48463, size = 127, normalized size = 3.1 \begin{align*} \frac{7500 \, x^{4} - 5250 \, x^{3} - 4925 \, x^{2} + 682 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 555 \, x - 121}{3125 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.098975, size = 34, normalized size = 0.83 \begin{align*} \frac{12 x^{3}}{25} - \frac{78 x^{2}}{125} + \frac{37 x}{625} + \frac{682 \log{\left (5 x + 3 \right )}}{3125} - \frac{121}{15625 x + 9375} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.3531, size = 77, normalized size = 1.88 \begin{align*} -\frac{1}{3125} \,{\left (5 \, x + 3\right )}^{3}{\left (\frac{186}{5 \, x + 3} - \frac{829}{{\left (5 \, x + 3\right )}^{2}} - 12\right )} - \frac{121}{3125 \,{\left (5 \, x + 3\right )}} - \frac{682}{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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