Optimal. Leaf size=38 \[ \frac{12 x}{125}-\frac{319}{625 (5 x+3)}-\frac{121}{1250 (5 x+3)^2}-\frac{128}{625} \log (5 x+3) \]
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Rubi [A] time = 0.0157388, antiderivative size = 38, 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} \[ \frac{12 x}{125}-\frac{319}{625 (5 x+3)}-\frac{121}{1250 (5 x+3)^2}-\frac{128}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (2+3 x)}{(3+5 x)^3} \, dx &=\int \left (\frac{12}{125}+\frac{121}{125 (3+5 x)^3}+\frac{319}{125 (3+5 x)^2}-\frac{128}{125 (3+5 x)}\right ) \, dx\\ &=\frac{12 x}{125}-\frac{121}{1250 (3+5 x)^2}-\frac{319}{625 (3+5 x)}-\frac{128}{625} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0168775, size = 37, normalized size = 0.97 \[ \frac{\frac{5 \left (600 x^3+420 x^2-782 x-515\right )}{(5 x+3)^2}-256 \log (10 x+6)}{1250} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 31, normalized size = 0.8 \begin{align*}{\frac{12\,x}{125}}-{\frac{121}{1250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{319}{1875+3125\,x}}-{\frac{128\,\ln \left ( 3+5\,x \right ) }{625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10953, size = 42, normalized size = 1.11 \begin{align*} \frac{12}{125} \, x - \frac{11 \,{\left (58 \, x + 37\right )}}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac{128}{625} \, \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 = 1.30331, size = 142, normalized size = 3.74 \begin{align*} \frac{3000 \, x^{3} + 3600 \, x^{2} - 256 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 2110 \, x - 2035}{1250 \,{\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 = 0.114629, size = 29, normalized size = 0.76 \begin{align*} \frac{12 x}{125} - \frac{638 x + 407}{6250 x^{2} + 7500 x + 2250} - \frac{128 \log{\left (5 x + 3 \right )}}{625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.34214, size = 36, normalized size = 0.95 \begin{align*} \frac{12}{125} \, x - \frac{11 \,{\left (58 \, x + 37\right )}}{250 \,{\left (5 \, x + 3\right )}^{2}} - \frac{128}{625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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