Optimal. Leaf size=38 \[ -\frac{18 x}{125}-\frac{64}{625 (5 x+3)}-\frac{11}{1250 (5 x+3)^2}+\frac{87}{625} \log (5 x+3) \]
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Rubi [A] time = 0.0162943, 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} \[ -\frac{18 x}{125}-\frac{64}{625 (5 x+3)}-\frac{11}{1250 (5 x+3)^2}+\frac{87}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)^2}{(3+5 x)^3} \, dx &=\int \left (-\frac{18}{125}+\frac{11}{125 (3+5 x)^3}+\frac{64}{125 (3+5 x)^2}+\frac{87}{125 (3+5 x)}\right ) \, dx\\ &=-\frac{18 x}{125}-\frac{11}{1250 (3+5 x)^2}-\frac{64}{625 (3+5 x)}+\frac{87}{625} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0176923, size = 39, normalized size = 1.03 \[ \frac{87}{625} \log (-3 (5 x+3))-\frac{900 x^3+1680 x^2+1172 x+295}{250 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 31, normalized size = 0.8 \begin{align*} -{\frac{18\,x}{125}}-{\frac{11}{1250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{64}{1875+3125\,x}}+{\frac{87\,\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 = 1.15606, size = 42, normalized size = 1.11 \begin{align*} -\frac{18}{125} \, x - \frac{128 \, x + 79}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{87}{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 = 1.55035, size = 142, normalized size = 3.74 \begin{align*} -\frac{4500 \, x^{3} + 5400 \, x^{2} - 174 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2260 \, x + 395}{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 = 0.114859, size = 29, normalized size = 0.76 \begin{align*} - \frac{18 x}{125} - \frac{128 x + 79}{6250 x^{2} + 7500 x + 2250} + \frac{87 \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 = 1.4638, size = 36, normalized size = 0.95 \begin{align*} -\frac{18}{125} \, x - \frac{128 \, x + 79}{250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{87}{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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